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Theorem sbceq2a 2768
 Description: Equality theorem for class substitution. Class version of sbequ12r 1652. (Contributed by NM, 4-Jan-2017.)
Assertion
Ref Expression
sbceq2a (A = x → ([A / x]φφ))

Proof of Theorem sbceq2a
StepHypRef Expression
1 sbceq1a 2767 . . 3 (x = A → (φ[A / x]φ))
21eqcoms 2040 . 2 (A = x → (φ[A / x]φ))
32bicomd 129 1 (A = x → ([A / x]φφ))
 Colors of variables: wff set class Syntax hints:   → wi 4   ↔ wb 98   = wceq 1242  [wsbc 2758 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-5 1333  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-8 1392  ax-4 1397  ax-17 1416  ax-i9 1420  ax-ial 1424  ax-ext 2019 This theorem depends on definitions:  df-bi 110  df-sb 1643  df-clab 2024  df-cleq 2030  df-clel 2033  df-sbc 2759 This theorem is referenced by: (None)
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