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

Theorem disjr 3813
 Description: Two ways of saying that two classes are disjoint. (Contributed by Jeff Madsen, 19-Jun-2011.)
Assertion
Ref Expression
disjr
Distinct variable groups:   ,   ,

Proof of Theorem disjr
StepHypRef Expression
1 incom 3634 . . 3
21eqeq1i 2411 . 2
3 disj 3812 . 2
42, 3bitri 251 1
 Colors of variables: wff setvar class Syntax hints:   wn 3   wb 186   wceq 1407   wcel 1844  wral 2756   cin 3415  c0 3740 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1641  ax-4 1654  ax-5 1727  ax-6 1773  ax-7 1816  ax-10 1863  ax-11 1868  ax-12 1880  ax-13 2028  ax-ext 2382 This theorem depends on definitions:  df-bi 187  df-an 371  df-tru 1410  df-ex 1636  df-nf 1640  df-sb 1766  df-clab 2390  df-cleq 2396  df-clel 2399  df-nfc 2554  df-ral 2761  df-v 3063  df-dif 3419  df-in 3423  df-nul 3741 This theorem is referenced by:  zfreg2  8058  kqdisj  20527  iccntr  21620  iooinlbub  36916  stoweidlem57  37220
 Copyright terms: Public domain W3C validator