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

Theorem disjr 3380
 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 3236 . . 3
21eqeq1i 2123 . 2
3 disj 3379 . 2
42, 3bitri 183 1
 Colors of variables: wff set class Syntax hints:   wn 3   wb 104   wceq 1314   wcel 1463  wral 2391   cin 3038  c0 3331 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-in1 586  ax-in2 587  ax-io 681  ax-5 1406  ax-7 1407  ax-gen 1408  ax-ie1 1452  ax-ie2 1453  ax-8 1465  ax-10 1466  ax-11 1467  ax-i12 1468  ax-bndl 1469  ax-4 1470  ax-17 1489  ax-i9 1493  ax-ial 1497  ax-i5r 1498  ax-ext 2097 This theorem depends on definitions:  df-bi 116  df-tru 1317  df-nf 1420  df-sb 1719  df-clab 2102  df-cleq 2108  df-clel 2111  df-nfc 2245  df-ral 2396  df-v 2660  df-dif 3041  df-in 3045  df-nul 3332 This theorem is referenced by: (None)
 Copyright terms: Public domain W3C validator