Theorem indmss 3466

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 3461	1 |- ( ( _V \ A ) u. ( _V \ B ) ) C_ ( _V \ ( A i^i B ) )

Syntax hints:   _Vcvv 2802   \ cdif 3197   u. cun 3198   i^i cin 3199   C_ wss 3200

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 619  ax-in2 620  ax-io 716  ax-5 1495  ax-7 1496  ax-gen 1497  ax-ie1 1541  ax-ie2 1542  ax-8 1552  ax-10 1553  ax-11 1554  ax-i12 1555  ax-bndl 1557  ax-4 1558  ax-17 1574  ax-i9 1578  ax-ial 1582  ax-i5r 1583  ax-ext 2213

This theorem depends on definitions:  df-bi 117  df-tru 1400  df-nf 1509  df-sb 1811  df-clab 2218  df-cleq 2224  df-clel 2227  df-nfc 2363  df-v 2804  df-dif 3202  df-un 3204  df-in 3206  df-ss 3213

This theorem is referenced by:  difdifdirss  3579