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Theorem sbceq2a 3441
Description: Equality theorem for class substitution. Class version of sbequ12r 2110. (Contributed by NM, 4-Jan-2017.)
Assertion
Ref Expression
sbceq2a (𝐴 = 𝑥 → ([𝐴 / 𝑥]𝜑𝜑))

Proof of Theorem sbceq2a
StepHypRef Expression
1 sbceq1a 3440 . . 3 (𝑥 = 𝐴 → (𝜑[𝐴 / 𝑥]𝜑))
21eqcoms 2628 . 2 (𝐴 = 𝑥 → (𝜑[𝐴 / 𝑥]𝜑))
32bicomd 213 1 (𝐴 = 𝑥 → ([𝐴 / 𝑥]𝜑𝜑))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wb 196   = wceq 1481  [wsbc 3429
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1720  ax-4 1735  ax-5 1837  ax-6 1886  ax-7 1933  ax-9 1997  ax-12 2045  ax-ext 2600
This theorem depends on definitions:  df-bi 197  df-an 386  df-ex 1703  df-sb 1879  df-clab 2607  df-cleq 2613  df-clel 2616  df-sbc 3430
This theorem is referenced by:  tfindes  7047  rabssnn0fi  12768  indexa  33499  fdc  33512  fdc1  33513  alrimii  33895  tratrbVD  38917
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