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Theorem inass 3292
 Description: Associative law for intersection of classes. Exercise 9 of [TakeutiZaring] p. 17. (Contributed by NM, 3-May-1994.)
Assertion
Ref Expression
inass

Proof of Theorem inass
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 anass 399 . . . 4
2 elin 3265 . . . . 5
32anbi2i 453 . . . 4
41, 3bitr4i 186 . . 3
5 elin 3265 . . . 4
65anbi1i 454 . . 3
7 elin 3265 . . 3
84, 6, 73bitr4i 211 . 2
98ineqri 3275 1
 Colors of variables: wff set class Syntax hints:   wa 103   wceq 1332   wcel 1481   cin 3076 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 699  ax-5 1424  ax-7 1425  ax-gen 1426  ax-ie1 1470  ax-ie2 1471  ax-8 1483  ax-10 1484  ax-11 1485  ax-i12 1486  ax-bndl 1487  ax-4 1488  ax-17 1507  ax-i9 1511  ax-ial 1515  ax-i5r 1516  ax-ext 2122 This theorem depends on definitions:  df-bi 116  df-tru 1335  df-nf 1438  df-sb 1737  df-clab 2127  df-cleq 2133  df-clel 2136  df-nfc 2271  df-v 2692  df-in 3083 This theorem is referenced by:  in12  3293  in32  3294  in4  3298  indif2  3326  difun1  3342  dfrab3ss  3360  resres  4842  inres  4847  imainrect  4995  restco  12416  restopnb  12423
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