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Theorem disj3 3272
 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 pm4.71 369 . . . 4
2 eldif 2927 . . . . 5
32bibi2i 216 . . . 4
41, 3bitr4i 176 . . 3
54albii 1359 . 2
6 disj1 3270 . 2
7 dfcleq 2034 . 2
85, 6, 73bitr4i 201 1
 Colors of variables: wff set class Syntax hints:   wn 3   wi 4   wa 97   wb 98  wal 1241   wceq 1243   wcel 1393   cdif 2914   cin 2916  c0 3224 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 544  ax-in2 545  ax-io 630  ax-5 1336  ax-7 1337  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-8 1395  ax-10 1396  ax-11 1397  ax-i12 1398  ax-bndl 1399  ax-4 1400  ax-17 1419  ax-i9 1423  ax-ial 1427  ax-i5r 1428  ax-ext 2022 This theorem depends on definitions:  df-bi 110  df-tru 1246  df-nf 1350  df-sb 1646  df-clab 2027  df-cleq 2033  df-clel 2036  df-nfc 2167  df-ral 2311  df-v 2559  df-dif 2920  df-in 2924  df-nul 3225 This theorem is referenced by:  disjel  3274  disj4im  3276  uneqdifeqim  3308  difprsn1  3503  diftpsn3  3505  orddif  4271  phpm  6327
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