Theorem axfrege52a 38150

Description: Justification for ax-frege52a 38151. (Contributed by RP, 17-Apr-2020.)

Assertion

Ref	Expression
axfrege52a	|- ( ( ph <-> ps ) -> (if- ( ph , th , ch ) -> if- ( ps , th , ch ) ) )

Proof of Theorem axfrege52a

Step	Hyp	Ref	Expression
1		ifpbi1 37822	. 2 |- ( ( ph <-> ps ) -> (if- ( ph , th , ch ) <-> if- ( ps , th , ch ) ) )
2	1	biimpd 219	1 |- ( ( ph <-> ps ) -> (if- ( ph , th , ch ) -> if- ( ps , th , ch ) ) )

Syntax hints:   -> wi 4   <-> wb 196  if-wif 1012

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 197  df-or 385  df-an 386  df-ifp 1013

This theorem is referenced by: (None)