Theorem indm 4247

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 4241	1 ⊢ (V ∖ (𝐴 ∩ 𝐵)) = ((V ∖ 𝐴) ∪ (V ∖ 𝐵))

This proof depends on syntax axioms:   = wceq 1570  Vcvv 3453   ∖ cdif 3899   ∪ cun 3900   ∩ cin 3901

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1828  ax-4 1842  ax-5 1943  ax-6 2000  ax-7 2041  ax-8 2147  ax-9 2155  ax-ext 2734

This proof depends on definitions:  df-bi 210  df-an 402  df-or 862  df-tru 1573  df-ex 1813  df-sb 2100  df-clab 2741  df-cleq 2754  df-clel 2837  df-rab 3415  df-v 3455  df-dif 3905  df-un 3907  df-in 3909

This theorem is used by:  difdifdir  4450