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Theorem ceqsexv2d 23178
 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 2836 . . 3
54biimpri 197 . 2
6 simpr 447 . . 3
76eximi 1566 . 2
81, 5, 7mp2b 9 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 176   wa 358  wex 1531   wceq 1632   wcel 1696  cvv 2801 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1536  ax-5 1547  ax-17 1606  ax-9 1644  ax-8 1661  ax-6 1715  ax-11 1727  ax-ext 2277 This theorem depends on definitions:  df-bi 177  df-an 360  df-ex 1532  df-nf 1535  df-sb 1639  df-clab 2283  df-cleq 2289  df-clel 2292  df-v 2803
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