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Theorem opprc2 4190
 Description: Expansion of an ordered pair when the second member is a proper class. See also opprc 4188. (Contributed by NM, 15-Nov-1994.) (Revised by Mario Carneiro, 26-Apr-2015.)
Assertion
Ref Expression
opprc2

Proof of Theorem opprc2
StepHypRef Expression
1 simpr 461 . . 3
21con3i 135 . 2
3 opprc 4188 . 2
42, 3syl 16 1
 Colors of variables: wff setvar class Syntax hints:   wn 3   wi 4   wa 369   wceq 1370   wcel 1758  cvv 3076  c0 3744  cop 3990 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1592  ax-4 1603  ax-5 1671  ax-6 1710  ax-7 1730  ax-10 1777  ax-11 1782  ax-12 1794  ax-13 1955  ax-ext 2432 This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-3an 967  df-tru 1373  df-ex 1588  df-nf 1591  df-sb 1703  df-clab 2440  df-cleq 2446  df-clel 2449  df-nfc 2604  df-v 3078  df-dif 3438  df-in 3442  df-ss 3449  df-nul 3745  df-if 3899  df-op 3991 This theorem is referenced by:  dmsnopss  5418  strle1  14387
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