Theorem subiml-P2.8a.SH 129

Description: Inference from subiml-P2.8a 128.

Hypothesis

Ref	Expression
subiml-P2.8a.SH.1	⊢ (𝜑 ↔ 𝜓)

Assertion

Ref	Expression
subiml-P2.8a.SH	⊢ ((𝜑 → 𝜒) ↔ (𝜓 → 𝜒))

Proof of Theorem subiml-P2.8a.SH

Step	Hyp	Ref	Expression
1		subiml-P2.8a.SH.1	. 2 ⊢ (𝜑 ↔ 𝜓)
2		subiml-P2.8a 128	. 2 ⊢ ((𝜑 ↔ 𝜓) → ((𝜑 → 𝜒) ↔ (𝜓 → 𝜒)))
3	1, 2	ax-MP 14	1 ⊢ ((𝜑 → 𝜒) ↔ (𝜓 → 𝜒))

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:  rcp-NDSEP3  186  rcp-NDSEP4  187  rcp-NDSEP5  188  rcp-NDJOIN3  189  rcp-NDJOIN4  190  rcp-NDJOIN5  191