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Theorem ceqsalg 3134
 Description: A representation of explicit substitution of a class for a variable, inferred from an implicit substitution hypothesis. For an alternate proof, see ceqsalgALT 3135. (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:   ,

Proof of Theorem ceqsalg
StepHypRef Expression
1 ceqsalg.1 . 2
2 ceqsalg.2 . . 3
32ax-gen 1618 . 2
4 ceqsalt 3132 . 2
51, 3, 4mp3an12 1314 1
 Colors of variables: wff setvar class Syntax hints:  ->wi 4  <->wb 184  A.wal 1393  =wceq 1395  F/wnf 1616  e.wcel 1818 This theorem is referenced by:  ceqsal  3136  uniiunlem  3587  ralrnmpt2  6417  sucprcregOLD  8047  fimaxre3  10517  pmapglbx  35493 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-10 1837  ax-12 1854  ax-ext 2435 This theorem depends on definitions:  df-bi 185  df-an 371  df-3an 975  df-tru 1398  df-ex 1613  df-nf 1617  df-sb 1740  df-clab 2443  df-cleq 2449  df-clel 2452  df-v 3111
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