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Theorem ceqsex 3085
 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 487 . . 3
41, 3exlimi 1997 . 2
52biimprcd 229 . . . 4
61, 5alrimi 1957 . . 3
7 ceqsex.2 . . . 4
87isseti 3053 . . 3
9 exintr 1758 . . 3
106, 8, 9mpisyl 21 . 2
114, 10impbii 191 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wb 188   wa 371  wal 1444   wceq 1446  wex 1665  wnf 1669   wcel 1889  cvv 3047 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1671  ax-4 1684  ax-5 1760  ax-6 1807  ax-7 1853  ax-10 1917  ax-12 1935  ax-ext 2433 This theorem depends on definitions:  df-bi 189  df-an 373  df-tru 1449  df-ex 1666  df-nf 1670  df-sb 1800  df-clab 2440  df-cleq 2446  df-clel 2449  df-v 3049 This theorem is referenced by:  ceqsexv  3086  ceqsex2  3088
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