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Theorem ceqsrexv 2972
 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 2620 . . 3
2 an12 772 . . . 4
32exbii 1582 . . 3
41, 3bitr4i 243 . 2
5 eleq1 2413 . . . . 5
6 ceqsrexv.1 . . . . 5
75, 6anbi12d 691 . . . 4
87ceqsexgv 2971 . . 3
98bianabs 850 . 2
104, 9syl5bb 248 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wb 176   wa 358  wex 1541   wceq 1642   wcel 1710  wrex 2615 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-7 1734  ax-11 1746  ax-12 1925  ax-ext 2334 This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649  df-clab 2340  df-cleq 2346  df-clel 2349  df-nfc 2478  df-rex 2620  df-v 2861 This theorem is referenced by:  ceqsrexbv  2973  ceqsrex2v  2974  fnasrn  5417  f1oiso  5499
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