Theorem undm 3394

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 3388	1 |- ( _V \ ( A u. B ) ) = ( ( _V \ A ) i^i ( _V \ B ) )

Syntax hints:   = wceq 1353   _Vcvv 2738   \ cdif 3127   u. cun 3128   i^i cin 3129

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 614  ax-in2 615  ax-io 709  ax-5 1447  ax-7 1448  ax-gen 1449  ax-ie1 1493  ax-ie2 1494  ax-8 1504  ax-10 1505  ax-11 1506  ax-i12 1507  ax-bndl 1509  ax-4 1510  ax-17 1526  ax-i9 1530  ax-ial 1534  ax-i5r 1535  ax-ext 2159

This theorem depends on definitions:  df-bi 117  df-tru 1356  df-nf 1461  df-sb 1763  df-clab 2164  df-cleq 2170  df-clel 2173  df-nfc 2308  df-v 2740  df-dif 3132  df-un 3134  df-in 3136

This theorem is referenced by:  difun1  3396