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Theorem ceqsex 2719
 Description: Elimination of an existential quantifier, using implicit substitution. (Contributed by NM, 2-Mar-1995.) (Revised by Mario Carneiro, 10-Oct-2016.)
Hypotheses
Ref Expression
ceqsex.1
ceqsex.2
ceqsex.3
Assertion
Ref Expression
ceqsex
Distinct variable group:   ,
Allowed substitution hints:   ()   ()

Proof of Theorem ceqsex
StepHypRef Expression
1 ceqsex.1 . . 3
2 ceqsex.3 . . . 4
32biimpa 294 . . 3
41, 3exlimi 1573 . 2
52biimprcd 159 . . . 4
61, 5alrimi 1502 . . 3
7 ceqsex.2 . . . 4
87isseti 2689 . . 3
9 exintr 1613 . . 3
106, 8, 9mpisyl 1422 . 2
114, 10impbii 125 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 103   wb 104  wal 1329   wceq 1331  wnf 1436  wex 1468   wcel 1480  cvv 2681 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 1423  ax-gen 1425  ax-ie1 1469  ax-ie2 1470  ax-8 1482  ax-4 1487  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-ext 2119 This theorem depends on definitions:  df-bi 116  df-nf 1437  df-sb 1736  df-clab 2124  df-cleq 2130  df-clel 2133  df-v 2683 This theorem is referenced by:  ceqsexv  2720  ceqsex2  2721
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