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Axiom ax-frege52c 37691
Description: One side of dfsbcq 3423. 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
StepHypRef Expression
1 cA . . 3 class 𝐴
2 cB . . 3 class 𝐵
31, 2wceq 1480 . 2 wff 𝐴 = 𝐵
4 wph . . . 4 wff 𝜑
5 vx . . . 4 setvar 𝑥
64, 5, 1wsbc 3421 . . 3 wff [𝐴 / 𝑥]𝜑
74, 5, 2wsbc 3421 . . 3 wff [𝐵 / 𝑥]𝜑
86, 7wi 4 . 2 wff ([𝐴 / 𝑥]𝜑[𝐵 / 𝑥]𝜑)
93, 8wi 4 1 wff (𝐴 = 𝐵 → ([𝐴 / 𝑥]𝜑[𝐵 / 𝑥]𝜑))
Colors of variables: wff setvar class
This axiom is referenced by:  frege52b  37692  frege53c  37717  frege57c  37723
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