Theorem: FOL.NV.C_14_14 (FOL/NV/Margaris/Prop.lean)

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

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

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

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

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