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Theorem oprcl 4244
 Description: If an ordered pair has an element, then its arguments are sets. (Contributed by Mario Carneiro, 26-Apr-2015.)
Assertion
Ref Expression
oprcl

Proof of Theorem oprcl
StepHypRef Expression
1 n0i 3795 . 2
2 opprc 4241 . 2
31, 2nsyl2 127 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wa 369   wceq 1379   wcel 1767  cvv 3118  c0 3790  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:  opth1  4726  opth  4727  0nelop  4743
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