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Theorem ceqsalg 2972
 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 2958 . . 3
2 nfa1 1806 . . . 4
3 ceqsalg.1 . . . 4
4 ceqsalg.2 . . . . . . 7
54biimpd 199 . . . . . 6
65a2i 13 . . . . 5
76sps 1770 . . . 4
82, 3, 7exlimd 1824 . . 3
91, 8syl5com 28 . 2
104biimprcd 217 . . 3
113, 10alrimi 1781 . 2
129, 11impbid1 195 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 177  wal 1549  wex 1550  wnf 1553   wceq 1652   wcel 1725 This theorem is referenced by:  ceqsal  2973  sbc6g  3178  uniiunlem  3423  ralrnmpt2  6176  sucprcreg  7559  fimaxre3  9949  pmapglbx  30503 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-6 1744  ax-11 1761  ax-ext 2416 This theorem depends on definitions:  df-bi 178  df-an 361  df-ex 1551  df-nf 1554  df-sb 1659  df-clab 2422  df-cleq 2428  df-clel 2431  df-v 2950
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