Theorem indmss 3406

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 3401	1 |- ( ( _V \ A ) u. ( _V \ B ) ) C_ ( _V \ ( A i^i B ) )

Syntax hints:   _Vcvv 2749   \ cdif 3138   u. cun 3139   i^i cin 3140   C_ wss 3141

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 615  ax-in2 616  ax-io 710  ax-5 1457  ax-7 1458  ax-gen 1459  ax-ie1 1503  ax-ie2 1504  ax-8 1514  ax-10 1515  ax-11 1516  ax-i12 1517  ax-bndl 1519  ax-4 1520  ax-17 1536  ax-i9 1540  ax-ial 1544  ax-i5r 1545  ax-ext 2169

This theorem depends on definitions:  df-bi 117  df-tru 1366  df-nf 1471  df-sb 1773  df-clab 2174  df-cleq 2180  df-clel 2183  df-nfc 2318  df-v 2751  df-dif 3143  df-un 3145  df-in 3147  df-ss 3154

This theorem is referenced by:  difdifdirss  3519