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Theorem ceqsrexv 2761
 Description: Elimination of a restricted existential quantifier, using implicit substitution. (Contributed by NM, 30-Apr-2004.)
Hypothesis
Ref Expression
ceqsrexv.1
Assertion
Ref Expression
ceqsrexv
Distinct variable groups:   ,   ,   ,
Allowed substitution hint:   ()

Proof of Theorem ceqsrexv
StepHypRef Expression
1 df-rex 2376 . . 3
2 an12 529 . . . 4
32exbii 1548 . . 3
41, 3bitr4i 186 . 2
5 eleq1 2157 . . . . 5
6 ceqsrexv.1 . . . . 5
75, 6anbi12d 458 . . . 4
87ceqsexgv 2760 . . 3
98bianabs 579 . 2
104, 9syl5bb 191 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 103   wb 104   wceq 1296  wex 1433   wcel 1445  wrex 2371 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 668  ax-5 1388  ax-7 1389  ax-gen 1390  ax-ie1 1434  ax-ie2 1435  ax-8 1447  ax-10 1448  ax-11 1449  ax-i12 1450  ax-bndl 1451  ax-4 1452  ax-17 1471  ax-i9 1475  ax-ial 1479  ax-i5r 1480  ax-ext 2077 This theorem depends on definitions:  df-bi 116  df-tru 1299  df-nf 1402  df-sb 1700  df-clab 2082  df-cleq 2088  df-clel 2091  df-nfc 2224  df-rex 2376  df-v 2635 This theorem is referenced by:  ceqsrexbv  2762  ceqsrex2v  2763  f1oiso  5643  creur  8517  creui  8518
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