Theorem indm 3513

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

Proof of Theorem indm

Step	Hyp	Ref	Expression
1		difindi 3509	1 |- (_V \ (A i^i B)) = ((_V \ A) u. (_V \ B))

Syntax hints:   = wceq 1642  _Vcvv 2859   \ cdif 3206   u. cun 3207   i^i cin 3208

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-7 1734  ax-11 1746  ax-12 1925  ax-ext 2334

This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-nan 1288  df-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649  df-clab 2340  df-cleq 2346  df-clel 2349  df-nfc 2478  df-v 2861  df-nin 3211  df-compl 3212  df-in 3213  df-un 3214  df-dif 3215

This theorem is referenced by:  difdifdir  3637