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

Theorem unixpss 4980
 Description: The double class union of a cross product is included in the union of its arguments. (Contributed by NM, 16-Sep-2006.)
Assertion
Ref Expression
unixpss

Proof of Theorem unixpss
StepHypRef Expression
1 xpsspw 4978 . . . . 5
21unissi 4030 . . . 4
3 unipw 4406 . . . 4
42, 3sseqtri 3372 . . 3
54unissi 4030 . 2
6 unipw 4406 . 2
75, 6sseqtri 3372 1
 Colors of variables: wff set class Syntax hints:   cun 3310   wss 3312  cpw 3791  cuni 4007   cxp 4868 This theorem is referenced by:  relfld  5387  filnetlem3  26363 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-14 1729  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2416  ax-sep 4322  ax-nul 4330  ax-pr 4395 This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-3an 938  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-clab 2422  df-cleq 2428  df-clel 2431  df-nfc 2560  df-ne 2600  df-v 2950  df-dif 3315  df-un 3317  df-in 3319  df-ss 3326  df-nul 3621  df-if 3732  df-pw 3793  df-sn 3812  df-pr 3813  df-op 3815  df-uni 4008  df-opab 4259  df-xp 4876
 Copyright terms: Public domain W3C validator