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Theorem sbceq2a 3803
Description: Equality theorem for class substitution. Class version of sbequ12r 2250. (Contributed by NM, 4-Jan-2017.)
Assertion
Ref Expression
sbceq2a (𝐴 = 𝑥 → ([𝐴 / 𝑥]𝜑𝜑))

Proof of Theorem sbceq2a
StepHypRef Expression
1 sbceq1a 3802 . . 3 (𝑥 = 𝐴 → (𝜑[𝐴 / 𝑥]𝜑))
21eqcoms 2743 . 2 (𝐴 = 𝑥 → (𝜑[𝐴 / 𝑥]𝜑))
32bicomd 223 1 (𝐴 = 𝑥 → ([𝐴 / 𝑥]𝜑𝜑))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wb 206   = wceq 1537  [wsbc 3791
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1792  ax-4 1806  ax-5 1908  ax-6 1965  ax-7 2005  ax-8 2108  ax-9 2116  ax-12 2175  ax-ext 2706
This theorem depends on definitions:  df-bi 207  df-an 396  df-ex 1777  df-sb 2063  df-clab 2713  df-cleq 2727  df-clel 2814  df-sbc 3792
This theorem is referenced by:  ralrnmptw  7114  tfindes  7884  rabssnn0fi  14024  indexa  37720  fdc  37732  fdc1  37733  alrimii  38106  tratrbVD  44859
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