Theorem frege67b 38206

Description: Lemma for frege68b 38207. Proposition 67 of [Frege1879] p. 54. (Contributed by RP, 24-Dec-2019.) (Proof modification is discouraged.)

Assertion

Ref	Expression
frege67b	|- ( ( ( A. x ph <-> ps ) -> ( ps -> A. x ph ) ) -> ( ( A. x ph <-> ps ) -> ( ps -> [ y / x ] ph ) ) )

Proof of Theorem frege67b

Step	Hyp	Ref	Expression
1		ax-frege58b 38195	. 2 |- ( A. x ph -> [ y / x ] ph )
2		frege7 38102	. 2 |- ( ( A. x ph -> [ y / x ] ph ) -> ( ( ( A. x ph <-> ps ) -> ( ps -> A. x ph ) ) -> ( ( A. x ph <-> ps ) -> ( ps -> [ y / x ] ph ) ) ) )
3	1, 2	ax-mp 5	1 |- ( ( ( A. x ph <-> ps ) -> ( ps -> A. x ph ) ) -> ( ( A. x ph <-> ps ) -> ( ps -> [ y / x ] ph ) ) )

Syntax hints:   -> wi 4   <-> wb 196   A.wal 1481   [wsb 1880

This theorem was proved from axioms:  ax-mp 5  ax-frege1 38084  ax-frege2 38085  ax-frege58b 38195

This theorem is referenced by:  frege68b  38207