Theorem undm 3489

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 3483	1 |- ( _V \ ( A u. B ) ) = ( ( _V \ A ) i^i ( _V \ B ) )

Syntax hints:   = wceq 1402   _Vcvv 2821   \ cdif 3217   u. cun 3218   i^i cin 3219

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 623  ax-in2 624  ax-io 721  ax-5 1500  ax-7 1501  ax-gen 1502  ax-ie1 1546  ax-ie2 1547  ax-8 1557  ax-10 1558  ax-11 1559  ax-i12 1560  ax-bndl 1562  ax-4 1563  ax-17 1579  ax-i9 1583  ax-ial 1587  ax-i5r 1588  ax-ext 2220

This theorem depends on definitions:  df-bi 117  df-tru 1405  df-nf 1514  df-sb 1816  df-clab 2225  df-cleq 2231  df-clel 2234  df-nfc 2381  df-v 2823  df-dif 3222  df-un 3224  df-in 3226

This theorem is referenced by:  difun1  3491