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Theorem inass 3465
 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 630 . . . 4
2 elin 3219 . . . . 5
32anbi2i 675 . . . 4
41, 3bitr4i 243 . . 3
5 elin 3219 . . . 4
65anbi1i 676 . . 3
7 elin 3219 . . 3
84, 6, 73bitr4i 268 . 2
98ineqri 3449 1
 Colors of variables: wff setvar class Syntax hints:   wa 358   wceq 1642   wcel 1710   cin 3208 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-7 1734  ax-11 1746  ax-12 1925  ax-ext 2334 This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-nan 1288  df-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649  df-clab 2340  df-cleq 2346  df-clel 2349  df-nfc 2478  df-v 2861  df-nin 3211  df-compl 3212  df-in 3213 This theorem is referenced by:  in12  3466  in32  3467  in4  3471  indif2  3498  difun1  3514  dfrab3ss  3533  dfif4  3673  ssfin  4470  resres  4980  inres  4985
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