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Theorem dfopg 4217
 Description: Value of the ordered pair when the arguments are sets. (Contributed by Mario Carneiro, 26-Apr-2015.) (Avoid depending on this detail.)
Assertion
Ref Expression
dfopg

Proof of Theorem dfopg
StepHypRef Expression
1 elex 3127 . 2
2 elex 3127 . 2
3 dfopif 4216 . . 3
4 iftrue 3951 . . 3
53, 4syl5eq 2520 . 2
61, 2, 5syl2an 477 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wa 369   wceq 1379   wcel 1767  cvv 3118  c0 3790  cif 3945  csn 4033  cpr 4035  cop 4039 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1601  ax-4 1612  ax-5 1680  ax-6 1719  ax-7 1739  ax-10 1786  ax-11 1791  ax-12 1803  ax-13 1968  ax-ext 2445 This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-3an 975  df-tru 1382  df-ex 1597  df-nf 1600  df-sb 1712  df-clab 2453  df-cleq 2459  df-clel 2462  df-nfc 2617  df-v 3120  df-dif 3484  df-in 3488  df-ss 3495  df-nul 3791  df-if 3946  df-op 4040 This theorem is referenced by:  dfop  4218  opnz  4724  opth1  4726  opth  4727  0nelop  4743  opwf  8242  rankopb  8282  wunop  9112  tskop  9161  gruop  9195  bj-elopg  34075
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