Theorem birev-P2.5b.SH 116

Description: Inference from birev-P2.5b 115.

Hypothesis

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

Assertion

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

Proof of Theorem birev-P2.5b.SH

Step	Hyp	Ref	Expression
1		birev-P2.5b.SH.1	. 2 ⊢ (𝜑 ↔ 𝜓)
2		birev-P2.5b 115	. 2 ⊢ ((𝜑 ↔ 𝜓) → (𝜓 → 𝜑))
3	1, 2	ax-MP 14	1 ⊢ (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:  cmb-P2.9c  138  orintl-P2.11a  146  orintr-P2.11b  148  true-P2.14  156