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Theorem rexab 3233
 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 2777 . 2
2 vex 3083 . . . . 5
3 ralab.1 . . . . 5
42, 3elab 3217 . . . 4
54anbi1i 699 . . 3
65exbii 1712 . 2
71, 6bitri 252 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wb 187   wa 370  wex 1657   wcel 1872  cab 2407  wrex 2772 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-11 1896  ax-12 1909  ax-13 2057  ax-ext 2401 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 2408  df-cleq 2414  df-clel 2417  df-nfc 2568  df-rex 2777  df-v 3082 This theorem is referenced by:  4sqlem12  14899  nofulllem5  30600  mblfinlem3  31943  mblfinlem4  31944  ismblfin  31945  itg2addnclem  31957  itg2addnc  31960  diophrex  35587
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