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Theorem indmss 3394
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 3389 1  |-  ( ( _V  \  A )  u.  ( _V  \  B ) )  C_  ( _V  \  ( A  i^i  B ) )
Colors of variables: wff set class
Syntax hints:   _Vcvv 2737    \ cdif 3126    u. cun 3127    i^i cin 3128    C_ wss 3129
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 614  ax-in2 615  ax-io 709  ax-5 1447  ax-7 1448  ax-gen 1449  ax-ie1 1493  ax-ie2 1494  ax-8 1504  ax-10 1505  ax-11 1506  ax-i12 1507  ax-bndl 1509  ax-4 1510  ax-17 1526  ax-i9 1530  ax-ial 1534  ax-i5r 1535  ax-ext 2159
This theorem depends on definitions:  df-bi 117  df-tru 1356  df-nf 1461  df-sb 1763  df-clab 2164  df-cleq 2170  df-clel 2173  df-nfc 2308  df-v 2739  df-dif 3131  df-un 3133  df-in 3135  df-ss 3142
This theorem is referenced by:  difdifdirss  3507
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