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Theorem invdif 3496
 Description: Intersection with universal complement. Remark in [Stoll] p. 20. (Contributed by NM, 17-Aug-2004.)
Assertion
Ref Expression
invdif (A ∩ (V B)) = (A B)

Proof of Theorem invdif
StepHypRef Expression
1 dfin2 3491 . 2 (A ∩ (V B)) = (A (V (V B)))
2 ddif 3398 . . 3 (V (V B)) = B
32difeq2i 3382 . 2 (A (V (V B))) = (A B)
41, 3eqtri 2373 1 (A ∩ (V B)) = (A B)
 Colors of variables: wff setvar class Syntax hints:   = wceq 1642  Vcvv 2859   ∖ 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 This theorem is referenced by:  indif2  3498  difundi  3507  difundir  3508  difindi  3509  difindir  3510  difun1  3514  undif1  3625  difdifdir  3637
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