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Theorem invdif 3371
Description: Intersection with universal complement. Remark in [Stoll] p. 20. (Contributed by NM, 17-Aug-2004.)
Assertion
Ref Expression
invdif  |-  ( A  i^i  ( _V  \  B ) )  =  ( A  \  B
)

Proof of Theorem invdif
StepHypRef Expression
1 dfin2 3366 . 2  |-  ( A  i^i  ( _V  \  B ) )  =  ( A  \  ( _V  \  ( _V  \  B ) ) )
2 ddif 3269 . . 3  |-  ( _V 
\  ( _V  \  B ) )  =  B
32difeq2i 3252 . 2  |-  ( A 
\  ( _V  \ 
( _V  \  B
) ) )  =  ( A  \  B
)
41, 3eqtri 2276 1  |-  ( A  i^i  ( _V  \  B ) )  =  ( A  \  B
)
Colors of variables: wff set class
Syntax hints:    = wceq 1619   _Vcvv 2757    \ cdif 3110    i^i cin 3112
This theorem is referenced by:  indif2  3373  difundi  3382  difundir  3383  difindi  3384  difindir  3385  difun1  3389  undif1  3490  difdifdir  3502  dfsup2  7149  dfsup2OLD  7150  nn0supp  9970  fsuppeq  26612
This theorem was proved from axioms:  ax-1 7  ax-2 8  ax-3 9  ax-mp 10  ax-5 1533  ax-6 1534  ax-7 1535  ax-gen 1536  ax-8 1623  ax-11 1624  ax-17 1628  ax-12o 1664  ax-10 1678  ax-9 1684  ax-4 1692  ax-16 1927  ax-ext 2237
This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-tru 1315  df-ex 1538  df-nf 1540  df-sb 1884  df-clab 2243  df-cleq 2249  df-clel 2252  df-nfc 2381  df-ral 2521  df-rab 2525  df-v 2759  df-dif 3116  df-in 3120
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