ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  op1sta Structured version   Unicode version

Theorem op1sta 4745
Description: Extract the first member of an ordered pair. (See op2nda 4748 to extract the second member and op1stb 4175 for an alternate version.) (Contributed by Raph Levien, 4-Dec-2003.)
Hypotheses
Ref Expression
cnvsn.1  _V
cnvsn.2  _V
Assertion
Ref Expression
op1sta  U. dom  {
<. ,  >. }

Proof of Theorem op1sta
StepHypRef Expression
1 cnvsn.2 . . . 4  _V
21dmsnop 4737 . . 3  dom  { <. ,  >. }  { }
32unieqi 3581 . 2  U. dom  {
<. ,  >. }  U. { }
4 cnvsn.1 . . 3  _V
54unisn 3587 . 2  U. { }
63, 5eqtri 2057 1  U. dom  {
<. ,  >. }
Colors of variables: wff set class
Syntax hints:   wceq 1242   wcel 1390   _Vcvv 2551   {csn 3367   <.cop 3370   U.cuni 3571   dom cdm 4288
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-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-14 1402  ax-17 1416  ax-i9 1420  ax-ial 1424  ax-i5r 1425  ax-ext 2019  ax-sep 3866  ax-pow 3918  ax-pr 3935
This theorem depends on definitions:  df-bi 110  df-3an 886  df-tru 1245  df-nf 1347  df-sb 1643  df-clab 2024  df-cleq 2030  df-clel 2033  df-nfc 2164  df-rex 2306  df-v 2553  df-un 2916  df-in 2918  df-ss 2925  df-pw 3353  df-sn 3373  df-pr 3374  df-op 3376  df-uni 3572  df-br 3756  df-dm 4298
This theorem is referenced by:  op1st  5715  fo1st  5726  f1stres  5728  xpassen  6240  xpdom2  6241
  Copyright terms: Public domain W3C validator