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Theorem ceqsalg 2582
 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 2568 . . 3
2 nfa1 1434 . . . 4
3 ceqsalg.1 . . . 4
4 ceqsalg.2 . . . . . . 7
54biimpd 132 . . . . . 6
65a2i 11 . . . . 5
76sps 1430 . . . 4
82, 3, 7exlimd 1488 . . 3
91, 8syl5com 26 . 2
104biimprcd 149 . . 3
113, 10alrimi 1415 . 2
129, 11impbid1 130 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 98  wal 1241   wceq 1243  wnf 1349  wex 1381   wcel 1393 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 1336  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-8 1395  ax-4 1400  ax-17 1419  ax-i9 1423  ax-ial 1427  ax-ext 2022 This theorem depends on definitions:  df-bi 110  df-nf 1350  df-sb 1646  df-clab 2027  df-cleq 2033  df-clel 2036  df-v 2559 This theorem is referenced by:  ceqsal  2583  sbc6g  2788  uniiunlem  3028  sucprcreg  4273  funimass4  5224  ralrnmpt2  5615
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