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

Theorem disjssun 3350
 Description: Subset relation for disjoint classes. (Contributed by NM, 25-Oct-2005.) (Proof shortened by Andrew Salmon, 26-Jun-2011.)
Assertion
Ref Expression
disjssun

Proof of Theorem disjssun
StepHypRef Expression
1 indi 3247 . . . . 5
21equncomi 3147 . . . 4
3 uneq2 3149 . . . . 5
4 un0 3320 . . . . 5
53, 4syl6eq 2137 . . . 4
62, 5syl5eq 2133 . . 3
76eqeq1d 2097 . 2
8 df-ss 3013 . 2
9 df-ss 3013 . 2
107, 8, 93bitr4g 222 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 104   wceq 1290   cun 2998   cin 2999   wss 3000  c0 3287 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-in1 580  ax-in2 581  ax-io 666  ax-5 1382  ax-7 1383  ax-gen 1384  ax-ie1 1428  ax-ie2 1429  ax-8 1441  ax-10 1442  ax-11 1443  ax-i12 1444  ax-bndl 1445  ax-4 1446  ax-17 1465  ax-i9 1469  ax-ial 1473  ax-i5r 1474  ax-ext 2071 This theorem depends on definitions:  df-bi 116  df-tru 1293  df-nf 1396  df-sb 1694  df-clab 2076  df-cleq 2082  df-clel 2085  df-nfc 2218  df-v 2622  df-dif 3002  df-un 3004  df-in 3006  df-ss 3013  df-nul 3288 This theorem is referenced by: (None)
 Copyright terms: Public domain W3C validator