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Theorem indmss 3409
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
StepHypRef Expression
1 difindiss 3404 1  |-  ( ( _V  \  A )  u.  ( _V  \  B ) )  C_  ( _V  \  ( A  i^i  B ) )
Colors of variables: wff set class
Syntax hints:   _Vcvv 2752    \ cdif 3141    u. cun 3142    i^i cin 3143    C_ wss 3144
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 1458  ax-7 1459  ax-gen 1460  ax-ie1 1504  ax-ie2 1505  ax-8 1515  ax-10 1516  ax-11 1517  ax-i12 1518  ax-bndl 1520  ax-4 1521  ax-17 1537  ax-i9 1541  ax-ial 1545  ax-i5r 1546  ax-ext 2171
This theorem depends on definitions:  df-bi 117  df-tru 1367  df-nf 1472  df-sb 1774  df-clab 2176  df-cleq 2182  df-clel 2185  df-nfc 2321  df-v 2754  df-dif 3146  df-un 3148  df-in 3150  df-ss 3157
This theorem is referenced by:  difdifdirss  3522
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