Theorem frege53c 38208

Description: Proposition 53 of [Frege1879] p. 50. (Contributed by RP, 24-Dec-2019.) (Proof modification is discouraged.)

Assertion

Ref	Expression
frege53c	|- ( [. A / x ]. ph -> ( A = B -> [. B / x ]. ph ) )

Proof of Theorem frege53c

Step	Hyp	Ref	Expression
1		ax-frege52c 38182	. 2 |- ( A = B -> ( [. A / x ]. ph -> [. B / x ]. ph ) )
2		ax-frege8 38103	. 2 |- ( ( A = B -> ( [. A / x ]. ph -> [. B / x ]. ph ) ) -> ( [. A / x ]. ph -> ( A = B -> [. B / x ]. ph ) ) )
3	1, 2	ax-mp 5	1 |- ( [. A / x ]. ph -> ( A = B -> [. B / x ]. ph ) )

Syntax hints:   -> wi 4   = wceq 1483   [.wsbc 3435

This theorem was proved from axioms:  ax-mp 5  ax-frege8 38103  ax-frege52c 38182

This theorem is referenced by:  frege55lem2c  38211  frege55c  38212  frege56c  38213  frege92  38249