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Theorem ceqsrex2v 2728
 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 393 . . . . . 6
21rexbii 2374 . . . . 5
3 r19.42v 2512 . . . . 5
42, 3bitri 182 . . . 4
54rexbii 2374 . . 3
6 ceqsrex2v.1 . . . . . 6
76anbi2d 452 . . . . 5
87rexbidv 2370 . . . 4
98ceqsrexv 2726 . . 3
105, 9syl5bb 190 . 2
11 ceqsrex2v.2 . . 3
1211ceqsrexv 2726 . 2
1310, 12sylan9bb 450 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 102   wb 103   wceq 1285   wcel 1434  wrex 2350 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-io 663  ax-5 1377  ax-7 1378  ax-gen 1379  ax-ie1 1423  ax-ie2 1424  ax-8 1436  ax-10 1437  ax-11 1438  ax-i12 1439  ax-bndl 1440  ax-4 1441  ax-17 1460  ax-i9 1464  ax-ial 1468  ax-i5r 1469  ax-ext 2064 This theorem depends on definitions:  df-bi 115  df-tru 1288  df-nf 1391  df-sb 1687  df-clab 2069  df-cleq 2075  df-clel 2078  df-nfc 2209  df-rex 2355  df-v 2604 This theorem is referenced by: (None)
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