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Theorem ssindif0 3823
 Description: Subclass expressed in terms of intersection with difference from the universal class. (Contributed by NM, 17-Sep-2003.)
Assertion
Ref Expression
ssindif0

Proof of Theorem ssindif0
StepHypRef Expression
1 disj2 3817 . 2
2 ddif 3575 . . 3
32sseq2i 3467 . 2
41, 3bitr2i 250 1
 Colors of variables: wff setvar class Syntax hints:   wb 184   wceq 1405  cvv 3059   cdif 3411   cin 3413   wss 3414  c0 3738 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1639  ax-4 1652  ax-5 1725  ax-6 1771  ax-7 1814  ax-10 1861  ax-11 1866  ax-12 1878  ax-13 2026  ax-ext 2380 This theorem depends on definitions:  df-bi 185  df-an 369  df-tru 1408  df-ex 1634  df-nf 1638  df-sb 1764  df-clab 2388  df-cleq 2394  df-clel 2397  df-nfc 2552  df-ral 2759  df-v 3061  df-dif 3417  df-in 3421  df-ss 3428  df-nul 3739 This theorem is referenced by:  setind  8197
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