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Theorem rexrab2 3267
 Description: Existential quantification over a class abstraction. (Contributed by Mario Carneiro, 3-Sep-2015.)
Hypothesis
Ref Expression
ralab2.1
Assertion
Ref Expression
rexrab2
Distinct variable groups:   ,   ,   ,   ,   ,

Proof of Theorem rexrab2
StepHypRef Expression
1 df-rab 2816 . . 3
21rexeqi 3059 . 2
3 ralab2.1 . . 3
43rexab2 3266 . 2
5 anass 649 . . . 4
65exbii 1667 . . 3
7 df-rex 2813 . . 3
86, 7bitr4i 252 . 2
92, 4, 83bitri 271 1
 Colors of variables: wff setvar class Syntax hints:  ->wi 4  <->wb 184  /\wa 369  E.wex 1612  e.wcel 1818  {cab 2442  E.wrex 2808  {crab 2811 This theorem is referenced by:  frminex  4864  sstotbnd3  30272 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-11 1842  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-nfc 2607  df-rex 2813  df-rab 2816
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