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

Theorem unopn 16978
 Description: The union of two open sets is open. (Contributed by Jeff Madsen, 2-Sep-2009.)
Assertion
Ref Expression
unopn

Proof of Theorem unopn
StepHypRef Expression
1 uniprg 4032 . . 3
213adant1 976 . 2
3 prssi 3956 . . . 4
4 uniopn 16972 . . . 4
53, 4sylan2 462 . . 3
653impb 1150 . 2
72, 6eqeltrrd 2513 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 360   w3a 937   wceq 1653   wcel 1726   cun 3320   wss 3322  cpr 3817  cuni 4017  ctop 16960 This theorem is referenced by:  txcld  17637  icccld  18803  comppfsc  26389 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1667  ax-8 1688  ax-6 1745  ax-7 1750  ax-11 1762  ax-12 1951  ax-ext 2419  ax-sep 4332 This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-3an 939  df-tru 1329  df-ex 1552  df-nf 1555  df-sb 1660  df-clab 2425  df-cleq 2431  df-clel 2434  df-nfc 2563  df-ral 2712  df-rex 2713  df-v 2960  df-un 3327  df-in 3329  df-ss 3336  df-pw 3803  df-sn 3822  df-pr 3823  df-uni 4018  df-top 16965
 Copyright terms: Public domain W3C validator