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Theorem difss 3393
 Description: Subclass relationship for class difference. Exercise 14 of [TakeutiZaring] p. 22. (Contributed by NM, 29-Apr-1994.)
Assertion
Ref Expression
difss (A B) A

Proof of Theorem difss
Dummy variable x is distinct from all other variables.
StepHypRef Expression
1 eldifi 3388 . 2 (x (A B) → x A)
21ssriv 3277 1 (A B) A
 Colors of variables: wff setvar class Syntax hints:   ∖ cdif 3206   ⊆ wss 3257 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-7 1734  ax-11 1746  ax-12 1925  ax-ext 2334 This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-nan 1288  df-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649  df-clab 2340  df-cleq 2346  df-clel 2349  df-nfc 2478  df-v 2861  df-nin 3211  df-compl 3212  df-in 3213  df-dif 3215  df-ss 3259 This theorem is referenced by:  difssd  3394  difss2  3395  ssdifss  3397  disj4  3599  0dif  3621  uneqdifeq  3638  difsnpss  3851  unidif  3923  iunxdif2  4014  imagekrelk  4273  nnsucelr  4428  sfinltfin  4535  vfinncvntsp  4549  vfinspsslem1  4550  vfinncsp  4554  resdif  5306  sbthlem1  6203
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