Intuitionistic Logic Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  ILE Home  >  Th. List  >  disj3 Unicode version

Theorem disj3 3442
 Description: Two ways of saying that two classes are disjoint. (Contributed by NM, 19-May-1998.)
Assertion
Ref Expression
disj3

Proof of Theorem disj3
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 pm4.71 387 . . . 4
2 eldif 3107 . . . . 5
32bibi2i 226 . . . 4
41, 3bitr4i 186 . . 3
54albii 1447 . 2
6 disj1 3440 . 2
7 dfcleq 2148 . 2
85, 6, 73bitr4i 211 1
 Colors of variables: wff set class Syntax hints:   wn 3   wi 4   wa 103   wb 104  wal 1330   wceq 1332   wcel 2125   cdif 3095   cin 3097  c0 3390 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 604  ax-in2 605  ax-io 699  ax-5 1424  ax-7 1425  ax-gen 1426  ax-ie1 1470  ax-ie2 1471  ax-8 1481  ax-10 1482  ax-11 1483  ax-i12 1484  ax-bndl 1486  ax-4 1487  ax-17 1503  ax-i9 1507  ax-ial 1511  ax-i5r 1512  ax-ext 2136 This theorem depends on definitions:  df-bi 116  df-tru 1335  df-nf 1438  df-sb 1740  df-clab 2141  df-cleq 2147  df-clel 2150  df-nfc 2285  df-ral 2437  df-v 2711  df-dif 3100  df-in 3104  df-nul 3391 This theorem is referenced by:  disjel  3444  uneqdifeqim  3475  difprsn1  3691  diftpsn3  3693  orddif  4500  phpm  6799
 Copyright terms: Public domain W3C validator