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Theorem sbceq2a 2988
Description: Equality theorem for class substitution. Class version of sbequ12r 1783. (Contributed by NM, 4-Jan-2017.)
Assertion
Ref Expression
sbceq2a (𝐴 = 𝑥 → ([𝐴 / 𝑥]𝜑𝜑))

Proof of Theorem sbceq2a
StepHypRef Expression
1 sbceq1a 2987 . . 3 (𝑥 = 𝐴 → (𝜑[𝐴 / 𝑥]𝜑))
21eqcoms 2192 . 2 (𝐴 = 𝑥 → (𝜑[𝐴 / 𝑥]𝜑))
32bicomd 141 1 (𝐴 = 𝑥 → ([𝐴 / 𝑥]𝜑𝜑))
Colors of variables: wff set class
Syntax hints:  wi 4  wb 105   = wceq 1364  [wsbc 2977
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-5 1458  ax-gen 1460  ax-ie1 1504  ax-ie2 1505  ax-8 1515  ax-4 1521  ax-17 1537  ax-i9 1541  ax-ial 1545  ax-ext 2171
This theorem depends on definitions:  df-bi 117  df-sb 1774  df-clab 2176  df-cleq 2182  df-clel 2185  df-sbc 2978
This theorem is referenced by: (None)
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