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Theorem inabs2 25241
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 3332 . . 3  |-  ( A  u.  B )  =  ( B  u.  A
)
21ineq2i 3380 . 2  |-  ( B  i^i  ( A  u.  B ) )  =  ( B  i^i  ( B  u.  A )
)
3 inabs 3413 . 2  |-  ( B  i^i  ( B  u.  A ) )  =  B
42, 3eqtri 2316 1  |-  ( B  i^i  ( A  u.  B ) )  =  B
Colors of variables: wff set class
Syntax hints:    = wceq 1632    u. cun 3163    i^i cin 3164
This theorem is referenced by:  hdrmp  25809
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1536  ax-5 1547  ax-17 1606  ax-9 1644  ax-8 1661  ax-6 1715  ax-7 1720  ax-11 1727  ax-12 1878  ax-ext 2277
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1310  df-ex 1532  df-nf 1535  df-sb 1639  df-clab 2283  df-cleq 2289  df-clel 2292  df-nfc 2421  df-v 2803  df-un 3170  df-in 3172  df-ss 3179
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