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Theorem sbceq2a 3597
Description: Equality theorem for class substitution. Class version of sbequ12r 2267. (Contributed by NM, 4-Jan-2017.)
Assertion
Ref Expression
sbceq2a (𝐴 = 𝑥 → ([𝐴 / 𝑥]𝜑𝜑))

Proof of Theorem sbceq2a
StepHypRef Expression
1 sbceq1a 3596 . . 3 (𝑥 = 𝐴 → (𝜑[𝐴 / 𝑥]𝜑))
21eqcoms 2778 . 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 1630  [wsbc 3585
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1869  ax-4 1884  ax-5 1990  ax-6 2056  ax-7 2092  ax-9 2153  ax-12 2202  ax-ext 2750
This theorem depends on definitions:  df-bi 197  df-an 383  df-ex 1852  df-sb 2049  df-clab 2757  df-cleq 2763  df-clel 2766  df-sbc 3586
This theorem is referenced by:  tfindes  7208  rabssnn0fi  12992  indexa  33853  fdc  33866  fdc1  33867  alrimii  34249  tratrbVD  39613
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