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

Theorem disj3 3245
Description: Two ways of saying that two classes are disjoint. (Contributed by NM, 19-May-1998.)
Assertion
Ref Expression
disj3  i^i  (/)  \

Proof of Theorem disj3
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 pm4.71 369 . . . 4
2 eldif 2900 . . . . 5  \
32bibi2i 216 . . . 4  \
41, 3bitr4i 176 . . 3  \
54albii 1335 . 2  \
6 disj1 3243 . 2  i^i  (/)
7 dfcleq 2012 . 2  \  \
85, 6, 73bitr4i 201 1  i^i  (/)  \
Colors of variables: wff set class
Syntax hints:   wn 3   wi 4   wa 97   wb 98  wal 1224   wceq 1226   wcel 1370    \ cdif 2887    i^i cin 2889   (/)c0 3197
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-in1 532  ax-in2 533  ax-io 617  ax-5 1312  ax-7 1313  ax-gen 1314  ax-ie1 1359  ax-ie2 1360  ax-8 1372  ax-10 1373  ax-11 1374  ax-i12 1375  ax-bnd 1376  ax-4 1377  ax-17 1396  ax-i9 1400  ax-ial 1405  ax-i5r 1406  ax-ext 2000
This theorem depends on definitions:  df-bi 110  df-tru 1229  df-nf 1326  df-sb 1624  df-clab 2005  df-cleq 2011  df-clel 2014  df-nfc 2145  df-ral 2285  df-v 2533  df-dif 2893  df-in 2897  df-nul 3198
This theorem is referenced by:  disjel  3247  disj4im  3249  uneqdifeqim  3281  difprsn1  3473  diftpsn3  3475
  Copyright terms: Public domain W3C validator