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Theorem rexab 2817
 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 2397 . 2
2 vex 2661 . . . . 5
3 ralab.1 . . . . 5
42, 3elab 2800 . . . 4
54anbi1i 451 . . 3
65exbii 1567 . 2
71, 6bitri 183 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 103   wb 104  wex 1451   wcel 1463  cab 2101  wrex 2392 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 681  ax-5 1406  ax-7 1407  ax-gen 1408  ax-ie1 1452  ax-ie2 1453  ax-8 1465  ax-10 1466  ax-11 1467  ax-i12 1468  ax-bndl 1469  ax-4 1470  ax-17 1489  ax-i9 1493  ax-ial 1497  ax-i5r 1498  ax-ext 2097 This theorem depends on definitions:  df-bi 116  df-tru 1317  df-nf 1420  df-sb 1719  df-clab 2102  df-cleq 2108  df-clel 2111  df-nfc 2245  df-rex 2397  df-v 2660 This theorem is referenced by:  rexrnmpo  5852
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