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

Theorem elopaba 6401
 Description: Membership in an ordered pair class builder. (Contributed by NM, 25-Feb-2014.) (Revised by Mario Carneiro, 31-Aug-2015.)
Hypothesis
Ref Expression
copsex2ga.1
Assertion
Ref Expression
elopaba
Distinct variable groups:   ,,   ,,
Allowed substitution hints:   (,)

Proof of Theorem elopaba
StepHypRef Expression
1 elopab 4454 . 2
2 copsex2ga.1 . . 3
32copsex2gb 6399 . 2
41, 3bitri 241 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 177   wa 359  wex 1550   wceq 1652   wcel 1725  cvv 2948  cop 3809  copab 4257   cxp 4868 This theorem is referenced by:  dicelvalN  31913 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-14 1729  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2416  ax-sep 4322  ax-nul 4330  ax-pr 4395 This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-3an 938  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-clab 2422  df-cleq 2428  df-clel 2431  df-nfc 2560  df-ne 2600  df-v 2950  df-dif 3315  df-un 3317  df-in 3319  df-ss 3326  df-nul 3621  df-if 3732  df-sn 3812  df-pr 3813  df-op 3815  df-opab 4259  df-xp 4876
 Copyright terms: Public domain W3C validator