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Theorem sbceq2a 3688
Description: Equality theorem for class substitution. Class version of sbequ12r 2181. (Contributed by NM, 4-Jan-2017.)
Assertion
Ref Expression
sbceq2a (𝐴 = 𝑥 → ([𝐴 / 𝑥]𝜑𝜑))

Proof of Theorem sbceq2a
StepHypRef Expression
1 sbceq1a 3687 . . 3 (𝑥 = 𝐴 → (𝜑[𝐴 / 𝑥]𝜑))
21eqcoms 2781 . 2 (𝐴 = 𝑥 → (𝜑[𝐴 / 𝑥]𝜑))
32bicomd 215 1 (𝐴 = 𝑥 → ([𝐴 / 𝑥]𝜑𝜑))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wb 198   = wceq 1508  [wsbc 3676
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1759  ax-4 1773  ax-5 1870  ax-6 1929  ax-7 1966  ax-8 2053  ax-9 2060  ax-12 2107  ax-ext 2745
This theorem depends on definitions:  df-bi 199  df-an 388  df-ex 1744  df-sb 2017  df-clab 2754  df-cleq 2766  df-clel 2841  df-sbc 3677
This theorem is referenced by:  tfindes  7392  rabssnn0fi  13168  indexa  34483  fdc  34495  fdc1  34496  alrimii  34874  tratrbVD  40648
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