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Theorem ceqsalg 3120
 Description: A representation of explicit substitution of a class for a variable, inferred from an implicit substitution hypothesis. For an alternate proof, see ceqsalgALT 3121. (Contributed by NM, 29-Oct-2003.) (Proof shortened by BJ, 29-Sep-2019.)
Hypotheses
Ref Expression
ceqsalg.1
ceqsalg.2
Assertion
Ref Expression
ceqsalg
Distinct variable group:   ,
Allowed substitution hints:   ()   ()   ()

Proof of Theorem ceqsalg
StepHypRef Expression
1 ceqsalg.1 . 2
2 ceqsalg.2 . . 3
32ax-gen 1605 . 2
4 ceqsalt 3118 . 2
51, 3, 4mp3an12 1315 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wb 184  wal 1381   wceq 1383  wnf 1603   wcel 1804 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1605  ax-4 1618  ax-5 1691  ax-6 1734  ax-7 1776  ax-10 1823  ax-12 1840  ax-ext 2421 This theorem depends on definitions:  df-bi 185  df-an 371  df-3an 976  df-tru 1386  df-ex 1600  df-nf 1604  df-sb 1727  df-clab 2429  df-cleq 2435  df-clel 2438  df-v 3097 This theorem is referenced by:  ceqsal  3122  uniiunlem  3573  ralrnmpt2  6402  sucprcregOLD  8029  fimaxre3  10499  pmapglbx  35233
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