Theorem frege61b 38200

Description: Lemma for frege65b 38204. Proposition 61 of [Frege1879] p. 52. (Contributed by RP, 24-Dec-2019.) (Proof modification is discouraged.)

Assertion

Ref	Expression
frege61b	|- ( ( [ x / y ] ph -> ps ) -> ( A. y ph -> ps ) )

Proof of Theorem frege61b

Step	Hyp	Ref	Expression
1		ax-frege58b 38195	. 2 |- ( A. y ph -> [ x / y ] ph )
2		frege9 38106	. 2 |- ( ( A. y ph -> [ x / y ] ph ) -> ( ( [ x / y ] ph -> ps ) -> ( A. y ph -> ps ) ) )
3	1, 2	ax-mp 5	1 |- ( ( [ x / y ] ph -> ps ) -> ( A. y ph -> ps ) )

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

This theorem was proved from axioms:  ax-mp 5  ax-frege1 38084  ax-frege2 38085  ax-frege8 38103  ax-frege58b 38195

This theorem is referenced by:  frege65b  38204