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Theorem ceqsrex2v 3073
 Description: Elimination of a restricted existential quantifier, using implicit substitution. (Contributed by NM, 29-Oct-2005.)
Hypotheses
Ref Expression
ceqsrex2v.1
ceqsrex2v.2
Assertion
Ref Expression
ceqsrex2v
Distinct variable groups:   ,,   ,,   ,   ,,   ,   ,
Allowed substitution hints:   (,)   ()   ()   ()

Proof of Theorem ceqsrex2v
StepHypRef Expression
1 anass 632 . . . . . 6
21rexbii 2732 . . . . 5
3 r19.42v 2864 . . . . 5
42, 3bitri 242 . . . 4
54rexbii 2732 . . 3
6 ceqsrex2v.1 . . . . . 6
76anbi2d 686 . . . . 5
87rexbidv 2728 . . . 4
98ceqsrexv 3071 . . 3
105, 9syl5bb 250 . 2
11 ceqsrex2v.2 . . 3
1211ceqsrexv 3071 . 2
1310, 12sylan9bb 682 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 178   wa 360   wceq 1653   wcel 1726  wrex 2708 This theorem is referenced by:  opiota  6537  brdom7disj  8411  brdom6disj  8412  lsmspsn  16158 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1667  ax-8 1688  ax-6 1745  ax-7 1750  ax-11 1762  ax-12 1951  ax-ext 2419 This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-tru 1329  df-ex 1552  df-nf 1555  df-sb 1660  df-clab 2425  df-cleq 2431  df-clel 2434  df-nfc 2563  df-rex 2713  df-v 2960
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