Metamath Proof Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  MPE Home  >  Th. List  >  rexrab2 Structured version   Unicode version

Theorem rexrab2 3104
 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:   ,   ,   ,   ,   ,
Allowed substitution hints:   ()   ()   ()   ()

Proof of Theorem rexrab2
StepHypRef Expression
1 df-rab 2716 . . 3
21rexeqi 2911 . 2
3 ralab2.1 . . 3
43rexab2 3103 . 2
5 anass 632 . . . 4
65exbii 1593 . . 3
7 df-rex 2713 . . 3
86, 7bitr4i 245 . 2
92, 4, 83bitri 264 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 178   wa 360  wex 1551   wcel 1726  cab 2424  wrex 2708  crab 2711 This theorem is referenced by:  frminex  4564  sstotbnd3  26487 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1667  ax-8 1688  ax-6 1745  ax-7 1750  ax-11 1762  ax-12 1951  ax-ext 2419 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 2425  df-cleq 2431  df-clel 2434  df-nfc 2563  df-rex 2713  df-rab 2716
 Copyright terms: Public domain W3C validator