Metamath Proof Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  MPE Home  >  Th. List  >  disj4 Unicode version

Theorem disj4 3875
 Description: Two ways of saying that two classes are disjoint. (Contributed by NM, 21-Mar-2004.)
Assertion
Ref Expression
disj4

Proof of Theorem disj4
StepHypRef Expression
1 disj3 3871 . 2
2 eqcom 2466 . 2
3 difss 3630 . . . 4
4 dfpss2 3588 . . . 4
53, 4mpbiran 918 . . 3
65con2bii 332 . 2
71, 2, 63bitri 271 1
 Colors of variables: wff setvar class Syntax hints:  -.wn 3  <->wb 184  =wceq 1395  \cdif 3472  i^icin 3474  C_wss 3475  C.wpss 3476   c0 3784 This theorem is referenced by:  marypha1lem  7913  infeq5i  8074  wilthlem2  23343 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-10 1837  ax-11 1842  ax-12 1854  ax-13 1999  ax-ext 2435 This theorem depends on definitions:  df-bi 185  df-an 371  df-tru 1398  df-ex 1613  df-nf 1617  df-sb 1740  df-clab 2443  df-cleq 2449  df-clel 2452  df-nfc 2607  df-ne 2654  df-ral 2812  df-v 3111  df-dif 3478  df-in 3482  df-ss 3489  df-pss 3491  df-nul 3785
 Copyright terms: Public domain W3C validator