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Theorem op2nda 5498
 Description: Extract the second member of an ordered pair. (See op1sta 5495 to extract the first member, op2ndb 5497 for an alternate version, and op2nd 6809 for the preferred version.) (Contributed by NM, 17-Feb-2004.) (Proof shortened by Andrew Salmon, 27-Aug-2011.)
Hypotheses
Ref Expression
cnvsn.1
cnvsn.2
Assertion
Ref Expression
op2nda

Proof of Theorem op2nda
StepHypRef Expression
1 cnvsn.1 . . . 4
21rnsnop 5494 . . 3
32unieqi 4258 . 2
4 cnvsn.2 . . 3
54unisn 4264 . 2
63, 5eqtri 2486 1
 Colors of variables: wff setvar class Syntax hints:  =wceq 1395  e.wcel 1818   cvv 3109  {csn 4029  <.cop 4035  U.cuni 4249  rancrn 5005 This theorem is referenced by:  elxp4  6744  elxp5  6745  op2nd  6809  fo2nd  6821  f2ndres  6823  ixpsnf1o  7529  xpassen  7631  xpdom2  7632  xpnnenOLD  13943 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-9 1822  ax-10 1837  ax-11 1842  ax-12 1854  ax-13 1999  ax-ext 2435  ax-sep 4573  ax-nul 4581  ax-pr 4691 This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-3an 975  df-tru 1398  df-ex 1613  df-nf 1617  df-sb 1740  df-eu 2286  df-mo 2287  df-clab 2443  df-cleq 2449  df-clel 2452  df-nfc 2607  df-ne 2654  df-ral 2812  df-rex 2813  df-rab 2816  df-v 3111  df-dif 3478  df-un 3480  df-in 3482  df-ss 3489  df-nul 3785  df-if 3942  df-sn 4030  df-pr 4032  df-op 4036  df-uni 4250  df-br 4453  df-opab 4511  df-xp 5010  df-rel 5011  df-cnv 5012  df-dm 5014  df-rn 5015
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