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Theorem rexab2 3266
 Description: Existential quantification over a class abstraction. (Contributed by Mario Carneiro, 3-Sep-2015.)
Hypothesis
Ref Expression
ralab2.1
Assertion
Ref Expression
rexab2
Distinct variable groups:   ,   ,   ,   ,
Allowed substitution hints:   ()   ()   ()

Proof of Theorem rexab2
StepHypRef Expression
1 df-rex 2813 . 2
2 nfsab1 2446 . . . 4
3 nfv 1708 . . . 4
42, 3nfan 1929 . . 3
5 nfv 1708 . . 3
6 eleq1 2529 . . . . 5
7 abid 2444 . . . . 5
86, 7syl6bb 261 . . . 4
9 ralab2.1 . . . 4
108, 9anbi12d 710 . . 3
114, 5, 10cbvex 2023 . 2
121, 11bitri 249 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wb 184   wa 369  wex 1613   wcel 1819  cab 2442  wrex 2808 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1619  ax-4 1632  ax-5 1705  ax-6 1748  ax-7 1791  ax-10 1838  ax-11 1843  ax-12 1855  ax-13 2000  ax-ext 2435 This theorem depends on definitions:  df-bi 185  df-an 371  df-ex 1614  df-nf 1618  df-sb 1741  df-clab 2443  df-cleq 2449  df-clel 2452  df-rex 2813 This theorem is referenced by:  rexrab2  3267  tmdgsum2  20721
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