Metamath Proof Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  MPE Home  >  Th. List  >  op1sta Unicode version

Theorem op1sta 5495
 Description: Extract the first member of an ordered pair. (See op2nda 5498 to extract the second member, op1stb 4722 for an alternate version, and op1st 6808 for the preferred version.) (Contributed by Raph Levien, 4-Dec-2003.)
Hypotheses
Ref Expression
cnvsn.1
cnvsn.2
Assertion
Ref Expression
op1sta

Proof of Theorem op1sta
StepHypRef Expression
1 cnvsn.2 . . . 4
21dmsnop 5487 . . 3
32unieqi 4258 . 2
4 cnvsn.1 . . 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  domcdm 5004 This theorem is referenced by:  elxp4  6744  op1st  6808  fo1st  6820  f1stres  6822  xpassen  7631  xpdom2  7632 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-clab 2443  df-cleq 2449  df-clel 2452  df-nfc 2607  df-ne 2654  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-dm 5014
 Copyright terms: Public domain W3C validator