Theorem indm 4243

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 4237	1 ⊢ (V ∖ (𝐴 ∩ 𝐵)) = ((V ∖ 𝐴) ∪ (V ∖ 𝐵))

This proof depends on syntax axioms:   = wceq 1569  Vcvv 3450   ∖ cdif 4045   ∩ cin 4089   ∪ cun 4149

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1827  ax-4 1841  ax-5 1942  ax-6 1999  ax-7 2040  ax-8 2146  ax-9 2154  ax-ext 2732

This proof depends on definitions:  df-bi 210  df-an 402  df-or 862  df-tru 1572  df-ex 1812  df-sb 2099  df-clab 2739  df-cleq 2752  df-clel 2835  df-rab 3413  df-v 3452  df-dif 4047  df-in 4091  df-un 4151

This theorem is used by:  difdifdir  4446