Axiom ax-frege52c 41385

Description: One side of dfsbcq 3713. 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]𝜑 → [𝐵 / 𝑥]𝜑))

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 1539	. 2 wff 𝐴 = 𝐵
4		wph	. . . 4 wff 𝜑
5		vx	. . . 4 setvar 𝑥
6	4, 5, 1	wsbc 3711	. . 3 wff [𝐴 / 𝑥]𝜑
7	4, 5, 2	wsbc 3711	. . 3 wff [𝐵 / 𝑥]𝜑
8	6, 7	wi 4	. 2 wff ([𝐴 / 𝑥]𝜑 → [𝐵 / 𝑥]𝜑)
9	3, 8	wi 4	1 wff (𝐴 = 𝐵 → ([𝐴 / 𝑥]𝜑 → [𝐵 / 𝑥]𝜑))

This axiom is referenced by:  frege52b  41386  frege53c  41411  frege57c  41417