Theorem opelvv 5051

Description: Ordered pair membership in the universal class of ordered pairs. (Contributed by NM, 22-Aug-2013.) (Revised by Mario Carneiro, 26-Apr-2015.)

Hypotheses

Ref	Expression
opelvv.1
opelvv.2

Assertion

Ref	Expression
opelvv

Proof of Theorem opelvv

Step	Hyp	Ref	Expression
1		opelvv.1	. 2
2		opelvv.2	. 2
3		opelxpi 5036	. 2
4	1, 2, 3	mp2an 672	1

Syntax hints:  e.wcel 1818  cvv 3109  <.cop 4035  X.cxp 5002

This theorem is referenced by:  relsnop  5112  relopabi  5133  1st2ndb  6838  eqop2  6841  evlfcl  15491  brtxp  29530  brpprod  29535  brsset  29539  brcart  29582  brcup  29589  brcap  29590  fusgraimpcl  32427  fusgraimpclALT  32429

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-ral 2812  df-rex 2813  df-rab 2816  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