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Theorem opprc2 3563
Description: Expansion of an ordered pair when the second member is a proper class. See also opprc 3561. (Contributed by NM, 15-Nov-1994.) (Revised by Mario Carneiro, 26-Apr-2015.)
Assertion
Ref Expression
opprc2  _V  <. ,  >.  (/)

Proof of Theorem opprc2
StepHypRef Expression
1 simpr 103 . . 3  _V  _V  _V
21con3i 561 . 2  _V  _V  _V
3 opprc 3561 . 2  _V  _V  <. ,  >.  (/)
42, 3syl 14 1  _V  <. ,  >.  (/)
Colors of variables: wff set class
Syntax hints:   wn 3   wi 4   wa 97   wceq 1242   wcel 1390   _Vcvv 2551   (/)c0 3218   <.cop 3370
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-in1 544  ax-in2 545  ax-io 629  ax-5 1333  ax-7 1334  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-8 1392  ax-10 1393  ax-11 1394  ax-i12 1395  ax-bndl 1396  ax-4 1397  ax-17 1416  ax-i9 1420  ax-ial 1424  ax-i5r 1425  ax-ext 2019
This theorem depends on definitions:  df-bi 110  df-3an 886  df-tru 1245  df-fal 1248  df-nf 1347  df-sb 1643  df-clab 2024  df-cleq 2030  df-clel 2033  df-nfc 2164  df-v 2553  df-dif 2914  df-nul 3219  df-op 3376
This theorem is referenced by: (None)
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