A connection mechanism for a copper pipe and a joint, the connection mechanism comprising: a copper pipe in which a projection including two inclined surfaces (5, 6) is formed in an end outer circumference; a joint, the joint including an inner diameter portion in which an end edge side of the projection of the copper pipe is inserted and including a nut engagement cylindrical portion in which a male screw is formed in an outer circumference on one end side, the joint pressing one of the inclined surfaces (5, 6) of the projection; and a nut including a nut body, the nut body including an inclined pressing portion and an opening in which a female screw screwed with the male screw of the nut engagement cylindrical portion is formed in an inner circumferential surface, the inclined pressing portion facing the joint in which the end edge side of the copper pipe is inserted in the inner diameter portion with the projection as a boundary, the inclined pressing portion being externally fitted on the copper pipe to press the other inclined surface (5, 6) of the projection, wherein the copper pipe and the joint are connected to each other by screwing the male screw of the nut engagement cylinder portion of the joint in the female screw of the nut body of the nut, a corner portion to a boundary with the inner diameter portion is formed in the joint, the corner portion abutting on one of the inclined surfaces (5, 6) of the projection, the corner portion being generated by forming a large diameter portion from an opening side of the inner circumferential surface of the nut engagement cylindrical portion, the joint includes a fitting cylindrical portion that is located in a center direction of the joint while being adjacent to the nut engagement cylindrical portion, the nut includes an extended cylindrical portion that extends from the nut body to be externally fitted on the copper pipe and a reinforcement cylindrical portion that extends toward an opposite direction to the extended cylindrical portion of the nut body to be externally fitted on the fitting cylindrical portion of the joint. a copper pipe in which a projection including two inclined surfaces (5, 6) is formed in an end outer circumference; a joint, the joint including an inner diameter portion in which an end edge side of the projection of the copper pipe is inserted and including a nut engagement cylindrical portion in which a male screw is formed in an outer circumference on one end side, the joint pressing one of the inclined surfaces (5, 6) of the projection; and a nut including a nut body, the nut body including an inclined pressing portion and an opening in which a female screw screwed with the male screw of the nut engagement cylindrical portion is formed in an inner circumferential surface, the inclined pressing portion facing the joint in which the end edge side of the copper pipe is inserted in the inner diameter portion with the projection as a boundary, the inclined pressing portion being externally fitted on the copper pipe to press the other inclined surface (5, 6) of the projection, wherein the copper pipe and the joint are connected to each other by screwing the male screw of the nut engagement cylinder portion of the joint in the female screw of the nut body of the nut, a corner portion to a boundary with the inner diameter portion is formed in the joint, the corner portion abutting on one of the inclined surfaces (5, 6) of the projection, the corner portion being generated by forming a large diameter portion from an opening side of the inner circumferential surface of the nut engagement cylindrical portion, the joint includes a fitting cylindrical portion that is located in a center direction of the joint while being adjacent to the nut engagement cylindrical portion, the nut includes an extended cylindrical portion that extends from the nut body to be externally fitted on the copper pipe and a reinforcement cylindrical portion that extends toward an opposite direction to the extended cylindrical portion of the nut body to be externally fitted on the fitting cylindrical portion of the joint.