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Theorem elvv 5063
 Description: Membership in universal class of ordered pairs. (Contributed by NM, 4-Jul-1994.)
Assertion
Ref Expression
elvv
Distinct variable group:   ,,

Proof of Theorem elvv
StepHypRef Expression
1 elxp 5021 . 2
2 vex 3112 . . . . 5
3 vex 3112 . . . . 5
42, 3pm3.2i 455 . . . 4
54biantru 505 . . 3
652exbii 1668 . 2
71, 6bitr4i 252 1
 Colors of variables: wff setvar class Syntax hints:  <->wb 184  /\wa 369  =wceq 1395  E.wex 1612  e.wcel 1818   cvv 3109  <.cop 4035  X.cxp 5002 This theorem is referenced by:  elvvv  5064  elvvuni  5065  elopaelxp  5077  ssrel  5096  elrel  5110  copsex2gb  5118  relop  5158  elreldm  5232  dmsnn0  5478  1stval2  6817  2ndval2  6818  1st2val  6826  2nd2val  6827  dfopab2  6854  dfoprab3s  6855  dftpos4  6993  tpostpos  6994  fundmen  7609  ssrelf  27466  dfdm5  29206  dfrn5  29207  brtxp2  29531  pprodss4v  29534  brpprod3a  29536  brimg  29587 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-9 1822  ax-10 1837  ax-11 1842  ax-12 1854  ax-13 1999  ax-ext 2435  ax-sep 4573  ax-nul 4581  ax-pr 4691 This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-3an 975  df-tru 1398  df-ex 1613  df-nf 1617  df-sb 1740  df-clab 2443  df-cleq 2449  df-clel 2452  df-nfc 2607  df-ne 2654  df-v 3111  df-dif 3478  df-un 3480  df-in 3482  df-ss 3489  df-nul 3785  df-if 3942  df-sn 4030  df-pr 4032  df-op 4036  df-opab 4511  df-xp 5010
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