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Theorem ceqsrexbv 2675
 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 2467 . 2
2 eleq1 2100 . . . . . . 7
32adantr 261 . . . . . 6
43pm5.32ri 428 . . . . 5
54bicomi 123 . . . 4
65baib 828 . . 3
76rexbiia 2339 . 2
8 ceqsrexv.1 . . . 4
98ceqsrexv 2674 . . 3
109pm5.32i 427 . 2
111, 7, 103bitr3i 199 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 97   wb 98   wceq 1243   wcel 1393  wrex 2307 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-io 630  ax-5 1336  ax-7 1337  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-8 1395  ax-10 1396  ax-11 1397  ax-i12 1398  ax-bndl 1399  ax-4 1400  ax-17 1419  ax-i9 1423  ax-ial 1427  ax-i5r 1428  ax-ext 2022 This theorem depends on definitions:  df-bi 110  df-tru 1246  df-nf 1350  df-sb 1646  df-clab 2027  df-cleq 2033  df-clel 2036  df-nfc 2167  df-rex 2312  df-v 2559 This theorem is referenced by:  frecsuclem3  5990
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