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Theorem ceqsalg 2718
 Description: A representation of explicit substitution of a class for a variable, inferred from an implicit substitution hypothesis. (Contributed by NM, 29-Oct-2003.) (Proof shortened by Andrew Salmon, 8-Jun-2011.)
Hypotheses
Ref Expression
ceqsalg.1
ceqsalg.2
Assertion
Ref Expression
ceqsalg
Distinct variable group:   ,
Allowed substitution hints:   ()   ()   ()

Proof of Theorem ceqsalg
StepHypRef Expression
1 elisset 2704 . . 3
2 nfa1 1522 . . . 4
3 ceqsalg.1 . . . 4
4 ceqsalg.2 . . . . . . 7
54biimpd 143 . . . . . 6
65a2i 11 . . . . 5
76sps 1518 . . . 4
82, 3, 7exlimd 1577 . . 3
91, 8syl5com 29 . 2
104biimprcd 159 . . 3
113, 10alrimi 1503 . 2
129, 11impbid1 141 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 104  wal 1330   wceq 1332  wnf 1437  wex 1469   wcel 1481 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-5 1424  ax-gen 1426  ax-ie1 1470  ax-ie2 1471  ax-8 1483  ax-4 1488  ax-17 1507  ax-i9 1511  ax-ial 1515  ax-ext 2122 This theorem depends on definitions:  df-bi 116  df-nf 1438  df-sb 1737  df-clab 2127  df-cleq 2133  df-clel 2136  df-v 2692 This theorem is referenced by:  ceqsal  2719  sbc6g  2938  uniiunlem  3191  sucprcreg  4473  funimass4  5481  ralrnmpo  5894
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