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Theorem ceqsrexbv 3148
 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 2922 . 2
2 eleq1 2494 . . . . . . 7
32adantr 466 . . . . . 6
43pm5.32ri 642 . . . . 5
54bicomi 205 . . . 4
65baib 911 . . 3
76rexbiia 2865 . 2
8 ceqsrexv.1 . . . 4
98ceqsrexv 3147 . . 3
109pm5.32i 641 . 2
111, 7, 103bitr3i 278 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wb 187   wa 370   wceq 1437   wcel 1872  wrex 2715 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 2063  ax-ext 2408 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 2415  df-cleq 2421  df-clel 2424  df-rex 2720  df-v 3024 This theorem is referenced by:  marypha2lem2  7903  txkgen  20609  ceqsrexv2  30308  eq0rabdioph  35531
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