Intuitionistic Logic Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  ILE Home  >  Th. List  >  opprc2 Unicode version

Theorem opprc2 3738
 Description: Expansion of an ordered pair when the second member is a proper class. See also opprc 3736. (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 109 . . 3
21con3i 622 . 2
3 opprc 3736 . 2
42, 3syl 14 1
 Colors of variables: wff set class Syntax hints:   wn 3   wi 4   wa 103   wceq 1332   wcel 2112  cvv 2691  c0 3370  cop 3537 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-in1 604  ax-in2 605  ax-io 699  ax-5 1424  ax-7 1425  ax-gen 1426  ax-ie1 1470  ax-ie2 1471  ax-8 1481  ax-10 1482  ax-11 1483  ax-i12 1484  ax-bndl 1486  ax-4 1487  ax-17 1503  ax-i9 1507  ax-ial 1511  ax-i5r 1512  ax-ext 2123 This theorem depends on definitions:  df-bi 116  df-3an 965  df-tru 1335  df-fal 1338  df-nf 1438  df-sb 1732  df-clab 2128  df-cleq 2134  df-clel 2137  df-nfc 2272  df-v 2693  df-dif 3080  df-nul 3371  df-op 3543 This theorem is referenced by: (None)
 Copyright terms: Public domain W3C validator