Axiom ax-frege52c 38182

Description: One side of dfsbcq 3437. Part of Axiom 52 of [Frege1879] p. 50. (Contributed by RP, 24-Dec-2019.) (New usage is discouraged.)

Assertion

Ref	Expression
ax-frege52c	|- ( A = B -> ( [. A / x ]. ph -> [. B / x ]. ph ) )

Detailed syntax breakdown of Axiom ax-frege52c

Step	Hyp	Ref	Expression
1		cA	. . 3 class A
2		cB	. . 3 class B
3	1, 2	wceq 1483	. 2 wff A = B
4		wph	. . . 4 wff ph
5		vx	. . . 4 setvar x
6	4, 5, 1	wsbc 3435	. . 3 wff [. A / x ]. ph
7	4, 5, 2	wsbc 3435	. . 3 wff [. B / x ]. ph
8	6, 7	wi 4	. 2 wff ( [. A / x ]. ph -> [. B / x ]. ph )
9	3, 8	wi 4	1 wff ( A = B -> ( [. A / x ]. ph -> [. B / x ]. ph ) )

This axiom is referenced by:  frege52b  38183  frege53c  38208  frege57c  38214