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

Theorem uniopel 4013
 Description: Ordered pair membership is inherited by class union. (Contributed by NM, 13-May-2008.) (Revised by Mario Carneiro, 26-Apr-2015.)
Hypotheses
Ref Expression
opthw.1
opthw.2
Assertion
Ref Expression
uniopel

Proof of Theorem uniopel
StepHypRef Expression
1 opthw.1 . . . 4
2 opthw.2 . . . 4
31, 2uniop 4012 . . 3
41, 2opi2 3990 . . 3
53, 4eqeltri 2152 . 2
6 elssuni 3631 . . 3
76sseld 2999 . 2
85, 7mpi 15 1
 Colors of variables: wff set class Syntax hints:   wi 4   wcel 1434  cvv 2602  cpr 3401  cop 3403  cuni 3603 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 3898  ax-pow 3950  ax-pr 3966 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-rex 2355  df-v 2604  df-un 2978  df-in 2980  df-ss 2987  df-pw 3386  df-sn 3406  df-pr 3407  df-op 3409  df-uni 3604 This theorem is referenced by:  dmrnssfld  4617  unielrel  4869
 Copyright terms: Public domain W3C validator