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Theorem disj4 3841
 Description: Two ways of saying that two classes are disjoint. (Contributed by NM, 21-Mar-2004.)
Assertion
Ref Expression
disj4

Proof of Theorem disj4
StepHypRef Expression
1 disj3 3837 . 2
2 eqcom 2431 . 2
3 difss 3592 . . . 4
4 dfpss2 3550 . . . 4
53, 4mpbiran 926 . . 3
65con2bii 333 . 2
71, 2, 63bitri 274 1
 Colors of variables: wff setvar class Syntax hints:   wn 3   wb 187   wceq 1437   cdif 3433   cin 3435   wss 3436   wpss 3437  c0 3761 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1665  ax-4 1678  ax-5 1748  ax-6 1794  ax-7 1839  ax-10 1887  ax-11 1892  ax-12 1905  ax-13 2053  ax-ext 2400 This theorem depends on definitions:  df-bi 188  df-an 372  df-tru 1440  df-ex 1660  df-nf 1664  df-sb 1787  df-clab 2408  df-cleq 2414  df-clel 2417  df-nfc 2572  df-ne 2620  df-ral 2780  df-v 3083  df-dif 3439  df-in 3443  df-ss 3450  df-pss 3452  df-nul 3762 This theorem is referenced by:  marypha1lem  7950  infeq5i  8144  wilthlem2  23981  topdifinffinlem  31691
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