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Theorem disjel 3873
 Description: A set can't belong to both members of disjoint classes. (Contributed by NM, 28-Feb-2015.)
Assertion
Ref Expression
disjel

Proof of Theorem disjel
StepHypRef Expression
1 disj3 3871 . . 3
2 eleq2 2530 . . . 4
3 eldifn 3626 . . . 4
42, 3syl6bi 228 . . 3
51, 4sylbi 195 . 2
65imp 429 1
 Colors of variables: wff setvar class Syntax hints:  -.wn 3  ->wi 4  /\wa 369  =wceq 1395  e.wcel 1818  \cdif 3472  i^icin 3474   c0 3784 This theorem is referenced by:  disjxun  4450  fvun1  5944  dedekindle  9766  fprodsplit  13770  dvasin  30103 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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