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Theorem axfrege52c 37078
Description: Justification for ax-frege52c 37079. (Contributed by RP, 24-Dec-2019.)
Assertion
Ref Expression
axfrege52c (𝐴 = 𝐵 → ([𝐴 / 𝑥]𝜑[𝐵 / 𝑥]𝜑))

Proof of Theorem axfrege52c
StepHypRef Expression
1 dfsbcq 3308 . 2 (𝐴 = 𝐵 → ([𝐴 / 𝑥]𝜑[𝐵 / 𝑥]𝜑))
21biimpd 217 1 (𝐴 = 𝐵 → ([𝐴 / 𝑥]𝜑[𝐵 / 𝑥]𝜑))
Colors of variables: wff setvar class
Syntax hints:  wi 4   = wceq 1474  [wsbc 3306
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1700  ax-4 1713  ax-5 1793  ax-ext 2494
This theorem depends on definitions:  df-bi 195  df-an 384  df-ex 1695  df-cleq 2507  df-clel 2510  df-sbc 3307
This theorem is referenced by: (None)
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