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Theorem opprc 3721
 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
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 df-op 3531 . 2
2 3simpa 978 . . . . 5
32con3i 621 . . . 4
43alrimiv 1846 . . 3
5 abeq0 3388 . . 3
64, 5sylibr 133 . 2
71, 6syl5eq 2182 1
 Colors of variables: wff set class Syntax hints:   wn 3   wi 4   wa 103   w3a 962  wal 1329   wceq 1331   wcel 1480  cab 2123  cvv 2681  c0 3358  csn 3522  cpr 3523  cop 3525 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 603  ax-in2 604  ax-io 698  ax-5 1423  ax-7 1424  ax-gen 1425  ax-ie1 1469  ax-ie2 1470  ax-8 1482  ax-10 1483  ax-11 1484  ax-i12 1485  ax-bndl 1486  ax-4 1487  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-i5r 1515  ax-ext 2119 This theorem depends on definitions:  df-bi 116  df-3an 964  df-tru 1334  df-fal 1337  df-nf 1437  df-sb 1736  df-clab 2124  df-cleq 2130  df-clel 2133  df-nfc 2268  df-v 2683  df-dif 3068  df-nul 3359  df-op 3531 This theorem is referenced by:  opprc1  3722  opprc2  3723  ovprc  5799
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