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Theorem opprc 4239
Description: Expansion of an ordered pair when either member is a proper class. (Contributed by Mario Carneiro, 26-Apr-2015.)
Assertion
Ref Expression
opprc

Proof of Theorem opprc
StepHypRef Expression
1 dfopif 4214 . 2
2 iffalse 3950 . 2
31, 2syl5eq 2510 1
Colors of variables: wff setvar class
Syntax hints:  -.wn 3  ->wi 4  /\wa 369  =wceq 1395  e.wcel 1818   cvv 3109   c0 3784  ifcif 3941  {csn 4029  {cpr 4031  <.cop 4035
This theorem is referenced by:  opprc1  4240  opprc2  4241  oprcl  4242  opnz  4723  opswap  5500  brabv  6342  brtpos  6983
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
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