Theorem indmss 3258

Description: De Morgan's law for intersection. In classical logic, this would be equality rather than subset, as in Theorem 5.2(13') of [Stoll] p. 19. (Contributed by Jim Kingdon, 27-Jul-2018.)

Assertion

Ref	Expression
indmss	|- ( ( _V \ A ) u. ( _V \ B ) ) C_ ( _V \ ( A i^i B ) )

Proof of Theorem indmss

Step	Hyp	Ref	Expression
1		difindiss 3253	1 |- ( ( _V \ A ) u. ( _V \ B ) ) C_ ( _V \ ( A i^i B ) )

Syntax hints:   _Vcvv 2619   \ cdif 2996   u. cun 2997   i^i cin 2998   C_ wss 2999

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-in1 579  ax-in2 580  ax-io 665  ax-5 1381  ax-7 1382  ax-gen 1383  ax-ie1 1427  ax-ie2 1428  ax-8 1440  ax-10 1441  ax-11 1442  ax-i12 1443  ax-bndl 1444  ax-4 1445  ax-17 1464  ax-i9 1468  ax-ial 1472  ax-i5r 1473  ax-ext 2070

This theorem depends on definitions:  df-bi 115  df-tru 1292  df-nf 1395  df-sb 1693  df-clab 2075  df-cleq 2081  df-clel 2084  df-nfc 2217  df-v 2621  df-dif 3001  df-un 3003  df-in 3005  df-ss 3012

This theorem is referenced by:  difdifdirss  3365