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Theorem rexrab 3000
Description: Existential quantification over a class abstraction. (Contributed by Jeff Madsen, 17-Jun-2011.) (Revised by Mario Carneiro, 3-Sep-2015.)
Hypothesis
Ref Expression
ralab.1
Assertion
Ref Expression
rexrab
Distinct variable groups:   ,   ,   ,
Allowed substitution hints:   (,)   ()   (,)   ()

Proof of Theorem rexrab
StepHypRef Expression
1 ralab.1 . . . . 5
21elrab 2994 . . . 4
32anbi1i 676 . . 3
4 anass 630 . . 3
53, 4bitri 240 . 2
65rexbii2 2643 1
Colors of variables: wff setvar class
Syntax hints:   wi 4   wb 176   wa 358   wcel 1710  wrex 2615  crab 2618
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-7 1734  ax-11 1746  ax-12 1925  ax-ext 2334
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649  df-clab 2340  df-cleq 2346  df-clel 2349  df-nfc 2478  df-rex 2620  df-rab 2623  df-v 2861
This theorem is referenced by:  phialllem1  4616
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