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Theorem axfrege52c 43214
Description: Justification for ax-frege52c 43215. (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 3774 . 2 (𝐴 = 𝐵 → ([𝐴 / 𝑥]𝜑[𝐵 / 𝑥]𝜑))
21biimpd 228 1 (𝐴 = 𝐵 → ([𝐴 / 𝑥]𝜑[𝐵 / 𝑥]𝜑))
Colors of variables: wff setvar class
Syntax hints:  wi 4   = wceq 1533  [wsbc 3772
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1789  ax-4 1803  ax-5 1905  ax-6 1963  ax-7 2003  ax-8 2100  ax-9 2108  ax-ext 2697
This theorem depends on definitions:  df-bi 206  df-an 396  df-ex 1774  df-cleq 2718  df-clel 2804  df-sbc 3773
This theorem is referenced by: (None)
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