Theorem birev-P2.5b.AC.SH 117

Description: Deductive Form of birev-P2.5b 115

Hypothesis

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

Assertion

Ref	Expression
birev-P2.5b.AC.SH	⊢ (𝛾 → (𝜓 → 𝜑))

Proof of Theorem birev-P2.5b.AC.SH

Step	Hyp	Ref	Expression
1		birev-P2.5b.AC.SH.1	. 2 ⊢ (𝛾 → (𝜑 ↔ 𝜓))
2		birev-P2.5b 115	. . . 4 ⊢ ((𝜑 ↔ 𝜓) → (𝜓 → 𝜑))
3	2	axL1.SH 30	. . 3 ⊢ (𝛾 → ((𝜑 ↔ 𝜓) → (𝜓 → 𝜑)))
4	3	rcp-FR1.SH 40	. 2 ⊢ ((𝛾 → (𝜑 ↔ 𝜓)) → (𝛾 → (𝜓 → 𝜑)))
5	1, 4	ax-MP 14	1 ⊢ (𝛾 → (𝜓 → 𝜑))

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:  ndbier-P3.15  180