Theorem bifwd-P2.5a.SH 112

Description: Inference from bifwd-P2.5a 111.

Hypothesis

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

Assertion

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

Proof of Theorem bifwd-P2.5a.SH

Step	Hyp	Ref	Expression
1		bifwd-P2.5a.SH.1	. 2 ⊢ (𝜑 ↔ 𝜓)
2		bifwd-P2.5a 111	. 2 ⊢ ((𝜑 ↔ 𝜓) → (𝜑 → 𝜓))
3	1, 2	ax-MP 14	1 ⊢ (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:  simpl-P2.9a  134  simpr-P2.9b  136  orelim-P2.11c  150  false-P2.15  159  rcp-NDSEP3  186  rcp-NDSEP4  187  rcp-NDSEP5  188  rcp-NDJOIN3  189  rcp-NDJOIN4  190  rcp-NDJOIN5  191