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Theorem compldif 4069
 Description: Complement in terms of difference. (Contributed by SF, 2-Jan-2018.)
Assertion
Ref Expression
compldif A = (V A)

Proof of Theorem compldif
StepHypRef Expression
1 df-dif 3215 . 2 (V A) = (V ∩ ∼ A)
2 incom 3448 . 2 (V ∩ ∼ A) = ( ∼ A ∩ V)
3 inv1 3577 . 2 ( ∼ A ∩ V) = ∼ A
41, 2, 33eqtrri 2378 1 A = (V A)
 Colors of variables: wff setvar class Syntax hints:   = wceq 1642  Vcvv 2859   ∼ ccompl 3205   ∖ cdif 3206   ∩ cin 3208 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 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:  complV  4070
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