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Theorem ceqsrexbv 3234
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:   ,   ,   ,

Proof of Theorem ceqsrexbv
StepHypRef Expression
1 r19.42v 3012 . 2
2 eleq1 2529 . . . . . . 7
32adantr 465 . . . . . 6
43pm5.32ri 638 . . . . 5
54bicomi 202 . . . 4
65baib 903 . . 3
76rexbiia 2958 . 2
8 ceqsrexv.1 . . . 4
98ceqsrexv 3233 . . 3
109pm5.32i 637 . 2
111, 7, 103bitr3i 275 1
Colors of variables: wff setvar class
Syntax hints:  ->wi 4  <->wb 184  /\wa 369  =wceq 1395  e.wcel 1818  E.wrex 2808
This theorem is referenced by:  marypha2lem2  7916  txkgen  20153  ceqsrexv2  29101  eq0rabdioph  30710
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-10 1837  ax-12 1854  ax-13 1999  ax-ext 2435
This theorem depends on definitions:  df-bi 185  df-an 371  df-tru 1398  df-ex 1613  df-nf 1617  df-sb 1740  df-clab 2443  df-cleq 2449  df-clel 2452  df-rex 2813  df-v 3111
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