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

Theorem ssunieq 4040
 Description: Relationship implying union. (Contributed by NM, 10-Nov-1999.)
Assertion
Ref Expression
ssunieq
Distinct variable groups:   ,   ,

Proof of Theorem ssunieq
StepHypRef Expression
1 elssuni 4035 . . 3
2 unissb 4037 . . . 4
32biimpri 198 . . 3
41, 3anim12i 550 . 2
5 eqss 3355 . 2
64, 5sylibr 204 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 359   wceq 1652   wcel 1725  wral 2697   wss 3312  cuni 4007 This theorem is referenced by:  unimax  4041  shsspwh  22738 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-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2416 This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  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-ral 2702  df-v 2950  df-in 3319  df-ss 3326  df-uni 4008
 Copyright terms: Public domain W3C validator