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Theorem ceqsrex2v 3206
 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 653 . . . . . 6
21rexbii 2924 . . . . 5
3 r19.42v 2980 . . . . 5
42, 3bitri 252 . . . 4
54rexbii 2924 . . 3
6 ceqsrex2v.1 . . . . . 6
76anbi2d 708 . . . . 5
87rexbidv 2936 . . . 4
98ceqsrexv 3204 . . 3
105, 9syl5bb 260 . 2
11 ceqsrex2v.2 . . 3
1211ceqsrexv 3204 . 2
1310, 12sylan9bb 704 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wb 187   wa 370   wceq 1437   wcel 1872  wrex 2772 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1663  ax-4 1676  ax-5 1752  ax-6 1798  ax-7 1843  ax-10 1891  ax-12 1909  ax-13 2057  ax-ext 2401 This theorem depends on definitions:  df-bi 188  df-an 372  df-tru 1440  df-ex 1658  df-nf 1662  df-sb 1791  df-clab 2408  df-cleq 2414  df-clel 2417  df-rex 2777  df-v 3082 This theorem is referenced by:  opiota  6866  brdom7disj  8966  brdom6disj  8967  lsmspsn  18306
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