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Theorem sbceq1a 2767
Description: Equality theorem for class substitution. Class version of sbequ12 1651. (Contributed by NM, 26-Sep-2003.)
Assertion
Ref Expression
sbceq1a (x = A → (φ[A / x]φ))

Proof of Theorem sbceq1a
StepHypRef Expression
1 sbid 1654 . 2 ([x / x]φφ)
2 dfsbcq2 2761 . 2 (x = A → ([x / x]φ[A / x]φ))
31, 2syl5bbr 183 1 (x = A → (φ[A / x]φ))
Colors of variables: wff set class
Syntax hints:  wi 4  wb 98   = wceq 1242  [wsb 1642  [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:  sbceq2a  2768  elrabsf  2795  cbvralcsf  2902  cbvrexcsf  2903  euotd  3982  ralrnmpt  5252  rexrnmpt  5253  riotass2  5437  riotass  5438  sbcopeq1a  5755  mpt2xopoveq  5796  indpi  6326  nn0ind-raph  8091  indstr  8272  fzrevral  8697  bj-intabssel  9197  bj-bdfindes  9337  bj-findes  9365
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