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Theorem ceqsrexbv 3072
 Description: Elimination of a restricted existential quantifier, using implicit substitution. (Contributed by Mario Carneiro, 14-Mar-2014.)
Hypothesis
Ref Expression
ceqsrexv.1
Assertion
Ref Expression
ceqsrexbv
Distinct variable groups:   ,   ,   ,
Allowed substitution hint:   ()

Proof of Theorem ceqsrexbv
StepHypRef Expression
1 r19.42v 2864 . 2
2 eleq1 2498 . . . . . . 7
32adantr 453 . . . . . 6
43pm5.32ri 621 . . . . 5
54bicomi 195 . . . 4
65baib 873 . . 3
76rexbiia 2740 . 2
8 ceqsrexv.1 . . . 4
98ceqsrexv 3071 . . 3
109pm5.32i 620 . 2
111, 7, 103bitr3i 268 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:  marypha2lem2  7444  txkgen  17689  ceqsrexv2  25186  eq0rabdioph  26849 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 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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