Intuitionistic Logic Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  ILE Home  >  Th. List  >  opi1 Unicode version

Theorem opi1 3995
 Description: One of the two elements in 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
opi1

Proof of Theorem opi1
StepHypRef Expression
1 opi1.1 . . . 4
21snex 3965 . . 3
32prid1 3506 . 2
4 opi1.2 . . 3
51, 4dfop 3577 . 2
63, 5eleqtrri 2155 1
 Colors of variables: wff set class Syntax hints:   wcel 1434  cvv 2602  csn 3406  cpr 3407  cop 3409 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-io 663  ax-5 1377  ax-7 1378  ax-gen 1379  ax-ie1 1423  ax-ie2 1424  ax-8 1436  ax-10 1437  ax-11 1438  ax-i12 1439  ax-bndl 1440  ax-4 1441  ax-14 1446  ax-17 1460  ax-i9 1464  ax-ial 1468  ax-i5r 1469  ax-ext 2064  ax-sep 3904  ax-pow 3956 This theorem depends on definitions:  df-bi 115  df-3an 922  df-tru 1288  df-nf 1391  df-sb 1687  df-clab 2069  df-cleq 2075  df-clel 2078  df-nfc 2209  df-v 2604  df-un 2978  df-in 2980  df-ss 2987  df-pw 3392  df-sn 3412  df-pr 3413  df-op 3415 This theorem is referenced by:  opth1  3999  opth  4000
 Copyright terms: Public domain W3C validator