Theorem undm 3421

Description: De Morgan's law for union. Theorem 5.2(13) of [Stoll] p. 19. (Contributed by NM, 18-Aug-2004.)

Assertion

Ref	Expression
undm	⊢ (V ∖ (𝐴 ∪ 𝐵)) = ((V ∖ 𝐴) ∩ (V ∖ 𝐵))

Proof of Theorem undm

Step	Hyp	Ref	Expression
1		difundi 3415	1 ⊢ (V ∖ (𝐴 ∪ 𝐵)) = ((V ∖ 𝐴) ∩ (V ∖ 𝐵))

Syntax hints:   = wceq 1364  Vcvv 2763   ∖ cdif 3154   ∪ cun 3155   ∩ cin 3156

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-in1 615  ax-in2 616  ax-io 710  ax-5 1461  ax-7 1462  ax-gen 1463  ax-ie1 1507  ax-ie2 1508  ax-8 1518  ax-10 1519  ax-11 1520  ax-i12 1521  ax-bndl 1523  ax-4 1524  ax-17 1540  ax-i9 1544  ax-ial 1548  ax-i5r 1549  ax-ext 2178

This theorem depends on definitions:  df-bi 117  df-tru 1367  df-nf 1475  df-sb 1777  df-clab 2183  df-cleq 2189  df-clel 2192  df-nfc 2328  df-v 2765  df-dif 3159  df-un 3161  df-in 3163

This theorem is referenced by:  difun1  3423