Theorem bifwd-P2.5a.AC.SH 113

Description: Deductive Form of bifwd-P2.5a 111

Hypothesis

Ref	Expression
bifwd-P2.5a.AC.SH.1	⊢ (𝛾 → (𝜑 ↔ 𝜓))

Assertion

Ref	Expression
bifwd-P2.5a.AC.SH	⊢ (𝛾 → (𝜑 → 𝜓))

Proof of Theorem bifwd-P2.5a.AC.SH

Step	Hyp	Ref	Expression
1		bifwd-P2.5a.AC.SH.1	. 2 ⊢ (𝛾 → (𝜑 ↔ 𝜓))
2		bifwd-P2.5a 111	. . . 4 ⊢ ((𝜑 ↔ 𝜓) → (𝜑 → 𝜓))
3	2	axL1.SH 30	. . 3 ⊢ (𝛾 → ((𝜑 ↔ 𝜓) → (𝜑 → 𝜓)))
4	3	rcp-FR1.SH 40	. 2 ⊢ ((𝛾 → (𝜑 ↔ 𝜓)) → (𝛾 → (𝜑 → 𝜓)))
5	1, 4	ax-MP 14	1 ⊢ (𝛾 → (𝜑 → 𝜓))

Syntax hints:   → wff-imp 10   ↔ wff-bi 104

This theorem was proved from axioms:  ax-L1 11  ax-L2 12  ax-L3 13  ax-MP 14

This theorem depends on definitions:  df-bi-D2.1 107

This theorem is referenced by:  ndbief-P3.14  179