Theorem axfrege52a 40195

Description: Justification for ax-frege52a 40196. (Contributed by RP, 17-Apr-2020.)

Assertion

Ref	Expression
axfrege52a	⊢ ((𝜑 ↔ 𝜓) → (if-(𝜑, 𝜃, 𝜒) → if-(𝜓, 𝜃, 𝜒)))

Proof of Theorem axfrege52a

Step	Hyp	Ref	Expression
1		ifpbi1 39836	. 2 ⊢ ((𝜑 ↔ 𝜓) → (if-(𝜑, 𝜃, 𝜒) ↔ if-(𝜓, 𝜃, 𝜒)))
2	1	biimpd 231	1 ⊢ ((𝜑 ↔ 𝜓) → (if-(𝜑, 𝜃, 𝜒) → if-(𝜓, 𝜃, 𝜒)))

Syntax hints:   → wi 4   ↔ wb 208  if-wif 1057

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This theorem depends on definitions:  df-bi 209  df-an 399  df-or 844  df-ifp 1058

This theorem is referenced by: (None)