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Theorem inabs 3162
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 3100 . 2  C_  u.
2 df-ss 2925 . 2 
C_  u.  i^i  u.
31, 2mpbi 133 1  i^i  u.
Colors of variables: wff set class
Syntax hints:   wceq 1242    u. cun 2909    i^i cin 2910    C_ wss 2911
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 629  ax-5 1333  ax-7 1334  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-8 1392  ax-10 1393  ax-11 1394  ax-i12 1395  ax-bndl 1396  ax-4 1397  ax-17 1416  ax-i9 1420  ax-ial 1424  ax-i5r 1425  ax-ext 2019
This theorem depends on definitions:  df-bi 110  df-tru 1245  df-nf 1347  df-sb 1643  df-clab 2024  df-cleq 2030  df-clel 2033  df-nfc 2164  df-v 2553  df-un 2916  df-in 2918  df-ss 2925
This theorem is referenced by: (None)
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