Theorem: FOL.NV.C_14_15 (FOL/NV/Margaris/Prop.lean)

State before:
P Q : Formula
Δ : Set Formula
h1 : IsDeduct Δ P
h2 : IsProof (P.imp_ Q)
⊢ IsDeduct Δ Q
Tactic:
apply IsDeduct.mp_ P
State after:
case a
P Q : Formula
Δ : Set Formula
h1 : IsDeduct Δ P
h2 : IsProof (P.imp_ Q)
⊢ IsDeduct Δ (P.imp_ Q)

case a
P Q : Formula
Δ : Set Formula
h1 : IsDeduct Δ P
h2 : IsProof (P.imp_ Q)
⊢ IsDeduct Δ P

State before:
case a
P Q : Formula
Δ : Set Formula
h1 : IsDeduct Δ P
h2 : IsProof (P.imp_ Q)
⊢ IsDeduct Δ (P.imp_ Q)
Tactic:
apply proof_imp_deduct
State after:
case a.h1
P Q : Formula
Δ : Set Formula
h1 : IsDeduct Δ P
h2 : IsProof (P.imp_ Q)
⊢ IsProof (P.imp_ Q)

State before:
case a.h1
P Q : Formula
Δ : Set Formula
h1 : IsDeduct Δ P
h2 : IsProof (P.imp_ Q)
⊢ IsProof (P.imp_ Q)
Tactic:
exact h2
State after:
no goals

State before:
case a
P Q : Formula
Δ : Set Formula
h1 : IsDeduct Δ P
h2 : IsProof (P.imp_ Q)
⊢ IsDeduct Δ P
Tactic:
exact h1
State after:
no goals