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Theorem ceqsexv2d 27524
 Description: Elimination of an existential quantifier, using implicit substitution. (Contributed by Thierry Arnoux, 10-Sep-2016.)
Hypotheses
Ref Expression
ceqsexv2d.1
ceqsexv2d.2
ceqsexv2d.3
Assertion
Ref Expression
ceqsexv2d
Distinct variable groups:   ,   ,
Allowed substitution hint:   ()

Proof of Theorem ceqsexv2d
StepHypRef Expression
1 ceqsexv2d.3 . 2
2 ceqsexv2d.1 . . . 4
3 ceqsexv2d.2 . . . 4
42, 3ceqsexv 3146 . . 3
54biimpri 206 . 2
6 exsimpr 1679 . 2
71, 5, 6mp2b 10 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wb 184   wa 369   wceq 1395  wex 1613   wcel 1819  cvv 3109 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1619  ax-4 1632  ax-5 1705  ax-6 1748  ax-7 1791  ax-10 1838  ax-12 1855  ax-ext 2435 This theorem depends on definitions:  df-bi 185  df-an 371  df-tru 1398  df-ex 1614  df-nf 1618  df-sb 1741  df-clab 2443  df-cleq 2449  df-clel 2452  df-v 3111 This theorem is referenced by: (None)
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