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Theorem ssdifss 3397
 Description: Preservation of a subclass relationship by class difference. (Contributed by NM, 15-Feb-2007.)
Assertion
Ref Expression
ssdifss (A B → (A C) B)

Proof of Theorem ssdifss
StepHypRef Expression
1 difss 3393 . 2 (A C) A
2 sstr 3280 . 2 (((A C) A A B) → (A C) B)
31, 2mpan 651 1 (A B → (A C) B)
 Colors of variables: wff setvar class Syntax hints:   → wi 4   ∖ 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:  ssdifssd  3404
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