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Theorem difsscompl 3549
 Description: A difference is a subset of the complement of its second argument. (Contributed by SF, 10-Mar-2015.)
Assertion
Ref Expression
difsscompl (A B) B

Proof of Theorem difsscompl
StepHypRef Expression
1 df-dif 3215 . 2 (A B) = (A ∩ ∼ B)
2 inss2 3476 . 2 (A ∩ ∼ B) B
31, 2eqsstri 3301 1 (A B) B
 Colors of variables: wff setvar class Syntax hints:   ∼ ccompl 3205   ∖ cdif 3206   ∩ cin 3208   ⊆ 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:  sbthlem1  6203
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