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Theorem difexg 4102
Description: The difference of two sets is a set. (Contributed by SF, 12-Jan-2015.)
Assertion
Ref Expression
difexg ((A V B W) → (A B) V)

Proof of Theorem difexg
StepHypRef Expression
1 df-dif 3215 . 2 (A B) = (A ∩ ∼ B)
2 complexg 4099 . . 3 (B W → ∼ B V)
3 inexg 4100 . . 3 ((A V B V) → (A ∩ ∼ B) V)
42, 3sylan2 460 . 2 ((A V B W) → (A ∩ ∼ B) V)
51, 4syl5eqel 2437 1 ((A V B W) → (A B) V)
Colors of variables: wff setvar class
Syntax hints:  wi 4   wa 358   wcel 1710  Vcvv 2859  ccompl 3205   cdif 3206  cin 3208
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  ax-nin 4078
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
This theorem is referenced by:  symdifexg  4103  difex  4107  imagekexg  4311  pwexg  4328  fullfunexg  5859  fnfreclem1  6317
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