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Theorem ceqsrexv 3233
 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:   ,   ,   ,

Proof of Theorem ceqsrexv
StepHypRef Expression
1 df-rex 2813 . . 3
2 an12 797 . . . 4
32exbii 1667 . . 3
41, 3bitr4i 252 . 2
5 eleq1 2529 . . . . 5
6 ceqsrexv.1 . . . . 5
75, 6anbi12d 710 . . . 4
87ceqsexgv 3232 . . 3
98bianabs 880 . 2
104, 9syl5bb 257 1
 Colors of variables: wff setvar class Syntax hints:  ->wi 4  <->wb 184  /\wa 369  =wceq 1395  E.wex 1612  e.wcel 1818  E.wrex 2808 This theorem is referenced by:  ceqsrexbv  3234  ceqsrex2v  3235  reuxfr2d  4675  f1oiso  6247  creur  10555  creui  10556  deg1ldg  22492  ulm2  22780  reuxfr3d  27388  rmxdiophlem  30957  expdiophlem1  30963  expdiophlem2  30964  eqlkr3  34826  diclspsn  36921 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-10 1837  ax-12 1854  ax-13 1999  ax-ext 2435 This theorem depends on definitions:  df-bi 185  df-an 371  df-tru 1398  df-ex 1613  df-nf 1617  df-sb 1740  df-clab 2443  df-cleq 2449  df-clel 2452  df-rex 2813  df-v 3111
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