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Theorem ceqsrex2v 2974
 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 630 . . . . . 6
21rexbii 2639 . . . . 5
3 r19.42v 2765 . . . . 5
42, 3bitri 240 . . . 4
54rexbii 2639 . . 3
6 ceqsrex2v.1 . . . . . 6
76anbi2d 684 . . . . 5
87rexbidv 2635 . . . 4
98ceqsrexv 2972 . . 3
105, 9syl5bb 248 . 2
11 ceqsrex2v.2 . . 3
1211ceqsrexv 2972 . 2
1310, 12sylan9bb 680 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wb 176   wa 358   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: (None)
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