New Foundations Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  NFE Home  >  Th. List  >  unidif Unicode version

Theorem unidif 3923
 Description: If the difference contains the largest members of , then the union of the difference is the union of . (Contributed by NM, 22-Mar-2004.)
Assertion
Ref Expression
unidif
Distinct variable groups:   ,,   ,,

Proof of Theorem unidif
StepHypRef Expression
1 uniss2 3922 . . 3
2 difss 3393 . . . 4
3 uniss 3912 . . . 4
42, 3ax-mp 8 . . 3
51, 4jctil 523 . 2
6 eqss 3287 . 2
75, 6sylibr 203 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wa 358   wceq 1642  wral 2614  wrex 2615   cdif 3206   wss 3257  cuni 3891 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-7 1734  ax-11 1746  ax-12 1925  ax-ext 2334 This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-nan 1288  df-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649  df-clab 2340  df-cleq 2346  df-clel 2349  df-nfc 2478  df-ral 2619  df-rex 2620  df-v 2861  df-nin 3211  df-compl 3212  df-in 3213  df-dif 3215  df-ss 3259  df-uni 3892 This theorem is referenced by: (None)
 Copyright terms: Public domain W3C validator