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Theorem inass 3147
 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 381 . . . 4
2 elin 3126 . . . . 5
32anbi2i 430 . . . 4
41, 3bitr4i 176 . . 3
5 elin 3126 . . . 4
65anbi1i 431 . . 3
7 elin 3126 . . 3
84, 6, 73bitr4i 201 . 2
98ineqri 3130 1
 Colors of variables: wff set class Syntax hints:   wa 97   wceq 1243   wcel 1393   cin 2916 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 2559  df-in 2924 This theorem is referenced by:  in12  3148  in32  3149  in4  3153  indif2  3181  difun1  3197  dfrab3ss  3215  resres  4624  inres  4629  imainrect  4766
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