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Theorem ceqsex 2992
 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 472 . . 3
41, 3exlimi 1822 . 2
52biimprcd 218 . . . 4
61, 5alrimi 1782 . . 3
7 ceqsex.2 . . . 4
87isseti 2964 . . 3
9 exintr 1625 . . 3
106, 8, 9ee10 1386 . 2
114, 10impbii 182 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 178   wa 360  wal 1550  wex 1551  wnf 1554   wceq 1653   wcel 1726  cvv 2958 This theorem is referenced by:  ceqsexv  2993  ceqsex2  2994 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1667  ax-8 1688  ax-6 1745  ax-11 1762  ax-ext 2419 This theorem depends on definitions:  df-bi 179  df-an 362  df-ex 1552  df-nf 1555  df-sb 1660  df-clab 2425  df-cleq 2431  df-clel 2434  df-v 2960
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