Intuitionistic Logic Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  ILE Home  >  Th. List  >  op2nda Unicode version

Theorem op2nda 5032
 Description: Extract the second member of an ordered pair. (See op1sta 5029 to extract the first member and op2ndb 5031 for an alternate 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 5028 . . 3
32unieqi 3755 . 2
4 cnvsn.2 . . 3
54unisn 3761 . 2
63, 5eqtri 2161 1
 Colors of variables: wff set class Syntax hints:   wceq 1332   wcel 1481  cvv 2690  csn 3533  cop 3536  cuni 3745   crn 4549 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 699  ax-5 1424  ax-7 1425  ax-gen 1426  ax-ie1 1470  ax-ie2 1471  ax-8 1483  ax-10 1484  ax-11 1485  ax-i12 1486  ax-bndl 1487  ax-4 1488  ax-14 1493  ax-17 1507  ax-i9 1511  ax-ial 1515  ax-i5r 1516  ax-ext 2122  ax-sep 4055  ax-pow 4107  ax-pr 4140 This theorem depends on definitions:  df-bi 116  df-3an 965  df-tru 1335  df-nf 1438  df-sb 1737  df-eu 2003  df-mo 2004  df-clab 2127  df-cleq 2133  df-clel 2136  df-nfc 2271  df-ral 2422  df-rex 2423  df-v 2692  df-un 3081  df-in 3083  df-ss 3090  df-pw 3518  df-sn 3539  df-pr 3540  df-op 3542  df-uni 3746  df-br 3939  df-opab 3999  df-xp 4554  df-rel 4555  df-cnv 4556  df-dm 4558  df-rn 4559 This theorem is referenced by:  elxp4  5035  elxp5  5036  op2nd  6054  fo2nd  6065  f2ndres  6067  ixpsnf1o  6639  xpassen  6733  xpdom2  6734
 Copyright terms: Public domain W3C validator