Theorem indm 4317

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

Assertion

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

Proof of Theorem indm

Step	Hyp	Ref	Expression
1		difindi 4311	1 ⊢ (V ∖ (𝐴 ∩ 𝐵)) = ((V ∖ 𝐴) ∪ (V ∖ 𝐵))

Syntax hints:   = wceq 1537  Vcvv 3488   ∖ cdif 3973   ∪ cun 3974   ∩ cin 3975

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1793  ax-4 1807  ax-5 1909  ax-6 1967  ax-7 2007  ax-8 2110  ax-9 2118  ax-ext 2711

This theorem depends on definitions:  df-bi 207  df-an 396  df-or 847  df-tru 1540  df-ex 1778  df-sb 2065  df-clab 2718  df-cleq 2732  df-clel 2819  df-rab 3444  df-v 3490  df-dif 3979  df-un 3981  df-in 3983

This theorem is referenced by:  difdifdir  4515