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Theorem opi2 4155
 Description: One of the two elements of an ordered pair. (Contributed by NM, 5-Aug-1993.) (Revised by Mario Carneiro, 26-Apr-2015.)
Hypotheses
Ref Expression
opi1.1
opi1.2
Assertion
Ref Expression
opi2

Proof of Theorem opi2
StepHypRef Expression
1 opi1.1 . . . 4
2 opi1.2 . . . 4
3 prexg 4133 . . . 4
41, 2, 3mp2an 422 . . 3
54prid2 3630 . 2
61, 2dfop 3704 . 2
75, 6eleqtrri 2215 1
 Colors of variables: wff set class Syntax hints:   wcel 1480  cvv 2686  csn 3527  cpr 3528  cop 3530 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-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-14 1492  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-i5r 1515  ax-ext 2121  ax-sep 4046  ax-pr 4131 This theorem depends on definitions:  df-bi 116  df-3an 964  df-tru 1334  df-nf 1437  df-sb 1736  df-clab 2126  df-cleq 2132  df-clel 2135  df-nfc 2270  df-v 2688  df-un 3075  df-sn 3533  df-pr 3534  df-op 3536 This theorem is referenced by:  uniopel  4178  opeluu  4371  elvvuni  4603
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