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Theorem disj3 3871
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 pm4.71 630 . . . 4
2 eldif 3485 . . . . 5
32bibi2i 313 . . . 4
41, 3bitr4i 252 . . 3
54albii 1640 . 2
6 disj1 3869 . 2
7 dfcleq 2450 . 2
85, 6, 73bitr4i 277 1
Colors of variables: wff setvar class
Syntax hints:  -.wn 3  ->wi 4  <->wb 184  /\wa 369  A.wal 1393  =wceq 1395  e.wcel 1818  \cdif 3472  i^icin 3474   c0 3784
This theorem is referenced by:  disjel  3873  disj4  3875  uneqdifeq  3916  difprsn1  4166  diftpsn3  4168  ssunsn2  4189  orddif  4976  php  7721  hartogslem1  7988  infeq5i  8074  cantnfp1lem3  8120  cantnfp1lem3OLD  8146  cda1dif  8577  infcda1  8594  ssxr  9675  dprd2da  17091  dmdprdsplit2lem  17094  ablfac1eulem  17123  lbsextlem4  17807  opsrtoslem2  18149  alexsublem  20544  volun  21955  lhop1lem  22414  ex-dif  25144  difeq  27416  imadifxp  27458  disjdsct  27521  probun  28358  ballotlemfp1  28430  finixpnum  30038  asindmre  30102  kelac2  31011  pwfi2f1o  31044  iccdifioo  31555  iccdifprioo  31556
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-10 1837  ax-11 1842  ax-12 1854  ax-13 1999  ax-ext 2435
This theorem depends on definitions:  df-bi 185  df-an 371  df-tru 1398  df-ex 1613  df-nf 1617  df-sb 1740  df-clab 2443  df-cleq 2449  df-clel 2452  df-nfc 2607  df-ral 2812  df-v 3111  df-dif 3478  df-in 3482  df-nul 3785
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