Theorem frege55a 38162

Description: Proposition 55 of [Frege1879] p. 50. (Contributed by RP, 24-Dec-2019.) (Proof modification is discouraged.)

Assertion

Ref	Expression
frege55a	|- ( ( ph <-> ps ) -> if- ( ps , ph , -. ph ) )

Proof of Theorem frege55a

Step	Hyp	Ref	Expression
1		frege54cor1a 38158	. 2 |- if- ( ph , ph , -. ph )
2		frege53a 38154	. 2 |- (if- ( ph , ph , -. ph ) -> ( ( ph <-> ps ) -> if- ( ps , ph , -. ph ) ) )
3	1, 2	ax-mp 5	1 |- ( ( ph <-> ps ) -> if- ( ps , ph , -. ph ) )

Syntax hints:   -. wn 3   -> 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  ax-frege8 38103  ax-frege28 38124  ax-frege52a 38151  ax-frege54a 38156

This theorem depends on definitions:  df-bi 197  df-or 385  df-an 386  df-ifp 1013

This theorem is referenced by:  frege55cor1a  38163