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Theorem sbceq1a 2750
Description: Equality theorem for class substitution. Class version of sbequ12 1636. (Contributed by NM, 26-Sep-2003.)
Assertion
Ref Expression
sbceq1a (x = A → (φ[A / x]φ))

Proof of Theorem sbceq1a
StepHypRef Expression
1 sbid 1639 . 2 ([x / x]φφ)
2 dfsbcq2 2744 . 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 1228  [wsb 1627  [wsbc 2741
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 1316  ax-gen 1318  ax-ie1 1363  ax-ie2 1364  ax-8 1376  ax-4 1381  ax-17 1400  ax-i9 1404  ax-ial 1409  ax-ext 2004
This theorem depends on definitions:  df-bi 110  df-sb 1628  df-clab 2009  df-cleq 2015  df-clel 2018  df-sbc 2742
This theorem is referenced by:  sbceq2a  2751  elrabsf  2778  cbvralcsf  2885  cbvrexcsf  2886  euotd  3965  ralrnmpt  5234  rexrnmpt  5235  riotass2  5418  riotass  5419  sbcopeq1a  5736  mpt2xopoveq  5777  bj-intabssel  7035  bj-bdfindes  7171  bj-findes  7199
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