Theorem subimr-P2.8b.SH 131

Description: Inference from subimr-P2.8b 130.

Hypothesis

Ref	Expression
subimr-P2.8b.SH.1	⊢ (𝜑 ↔ 𝜓)

Assertion

Ref	Expression
subimr-P2.8b.SH	⊢ ((𝜒 → 𝜑) ↔ (𝜒 → 𝜓))

Proof of Theorem subimr-P2.8b.SH

Step	Hyp	Ref	Expression
1		subimr-P2.8b.SH.1	. 2 ⊢ (𝜑 ↔ 𝜓)
2		subimr-P2.8b 130	. 2 ⊢ ((𝜑 ↔ 𝜓) → ((𝜒 → 𝜑) ↔ (𝜒 → 𝜓)))
3	1, 2	ax-MP 14	1 ⊢ ((𝜒 → 𝜑) ↔ (𝜒 → 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:  cmb-P2.9c  138