Theorem undm 3885

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 u. B ) ) = ( ( _V \ A ) i^i ( _V \ B ) )

Proof of Theorem undm

Step	Hyp	Ref	Expression
1		difundi 3879	1 |- ( _V \ ( A u. B ) ) = ( ( _V \ A ) i^i ( _V \ B ) )

Syntax hints:   = wceq 1483   _Vcvv 3200   \ cdif 3571   u. cun 3572   i^i cin 3573

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1722  ax-4 1737  ax-5 1839  ax-6 1888  ax-7 1935  ax-9 1999  ax-10 2019  ax-11 2034  ax-12 2047  ax-13 2246  ax-ext 2602

This theorem depends on definitions:  df-bi 197  df-or 385  df-an 386  df-tru 1486  df-ex 1705  df-nf 1710  df-sb 1881  df-clab 2609  df-cleq 2615  df-clel 2618  df-nfc 2753  df-ral 2917  df-rab 2921  df-v 3202  df-dif 3577  df-un 3579  df-in 3581

This theorem is referenced by:  difun1  3887