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Theorem inabs2 25138
Description: Absorption law for intersection. (Contributed by FL, 30-May-2014.)
Assertion
Ref Expression
inabs2  |-  ( B  i^i  ( A  u.  B ) )  =  B

Proof of Theorem inabs2
StepHypRef Expression
1 uncom 3319 . . 3  |-  ( A  u.  B )  =  ( B  u.  A
)
21ineq2i 3367 . 2  |-  ( B  i^i  ( A  u.  B ) )  =  ( B  i^i  ( B  u.  A )
)
3 inabs 3400 . 2  |-  ( B  i^i  ( B  u.  A ) )  =  B
42, 3eqtri 2303 1  |-  ( B  i^i  ( A  u.  B ) )  =  B
Colors of variables: wff set class
Syntax hints:    = wceq 1623    u. cun 3150    i^i cin 3151
This theorem is referenced by:  hdrmp  25706
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1533  ax-5 1544  ax-17 1603  ax-9 1635  ax-8 1643  ax-6 1703  ax-7 1708  ax-11 1715  ax-12 1866  ax-ext 2264
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1310  df-ex 1529  df-nf 1532  df-sb 1630  df-clab 2270  df-cleq 2276  df-clel 2279  df-nfc 2408  df-v 2790  df-un 3157  df-in 3159  df-ss 3166
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