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Theorem rexab 2703
 Description: Existential quantification over a class abstraction. (Contributed by Mario Carneiro, 23-Jan-2014.) (Revised by Mario Carneiro, 3-Sep-2015.)
Hypothesis
Ref Expression
ralab.1
Assertion
Ref Expression
rexab
Distinct variable groups:   ,   ,
Allowed substitution hints:   (,)   ()   (,)

Proof of Theorem rexab
StepHypRef Expression
1 df-rex 2312 . 2
2 vex 2560 . . . . 5
3 ralab.1 . . . . 5
42, 3elab 2687 . . . 4
54anbi1i 431 . . 3
65exbii 1496 . 2
71, 6bitri 173 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 97   wb 98  wex 1381   wcel 1393  cab 2026  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:  rexrnmpt2  5616
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