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Theorem inabs 3165
Description: Absorption law for intersection. (Contributed by NM, 16-Apr-2006.)
Assertion
Ref Expression
inabs  i^i  u.

Proof of Theorem inabs
StepHypRef Expression
1 ssun1 3103 . 2  C_  u.
2 df-ss 2928 . 2 
C_  u.  i^i  u.
31, 2mpbi 133 1  i^i  u.
Colors of variables: wff set class
Syntax hints:   wceq 1243    u. cun 2912    i^i cin 2913    C_ wss 2914
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-io 630  ax-5 1336  ax-7 1337  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-8 1395  ax-10 1396  ax-11 1397  ax-i12 1398  ax-bndl 1399  ax-4 1400  ax-17 1419  ax-i9 1423  ax-ial 1427  ax-i5r 1428  ax-ext 2022
This theorem depends on definitions:  df-bi 110  df-tru 1246  df-nf 1350  df-sb 1646  df-clab 2027  df-cleq 2033  df-clel 2036  df-nfc 2167  df-v 2556  df-un 2919  df-in 2921  df-ss 2928
This theorem is referenced by: (None)
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