Metamath Proof Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  MPE Home  >  Th. List  >  rexab Structured version   Unicode version

Theorem rexab 3103
 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 2717 . 2
2 vex 2965 . . . . 5
3 ralab.1 . . . . 5
42, 3elab 3088 . . . 4
54anbi1i 678 . . 3
65exbii 1593 . 2
71, 6bitri 242 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 178   wa 360  wex 1551   wcel 1727  cab 2428  wrex 2712 This theorem is referenced by:  4sqlem12  13355  nofulllem5  25692  mblfinlem3  26281  mblfinlem4  26282  ismblfin  26283  itg2addnclem  26294  itg2addnc  26297  diophrex  26872 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1668  ax-8 1689  ax-6 1746  ax-7 1751  ax-11 1763  ax-12 1953  ax-ext 2423 This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-tru 1329  df-ex 1552  df-nf 1555  df-sb 1660  df-clab 2429  df-cleq 2435  df-clel 2438  df-nfc 2567  df-rex 2717  df-v 2964
 Copyright terms: Public domain W3C validator