Theorem dfop 4216

Description: Value of an ordered pair when the arguments are sets, with the conclusion corresponding to Kuratowski's original definition. (Contributed by NM, 25-Jun-1998.) (Avoid depending on this detail.)

Hypotheses

Ref	Expression
dfop.1
dfop.2

Assertion

Ref	Expression
dfop

Proof of Theorem dfop

Step	Hyp	Ref	Expression
1		dfop.1	. 2
2		dfop.2	. 2
3		dfopg 4215	. 2
4	1, 2, 3	mp2an 672	1

Syntax hints:  =wceq 1395  e.wcel 1818  cvv 3109  {csn 4029  {cpr 4031  <.cop 4035

This theorem is referenced by:  opid  4236  elop  4718  opi1  4719  opi2  4720  op1stb  4722  opeqsn  4748  opeqpr  4749  uniop  4755  xpsspw  5121  xpsspwOLD  5122  relop  5158  funopg  5625

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-10 1837  ax-11 1842  ax-12 1854  ax-13 1999  ax-ext 2435

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-v 3111  df-dif 3478  df-in 3482  df-ss 3489  df-nul 3785  df-if 3942  df-op 4036