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Theorem in4 3713
Description: Rearrangement of intersection of 4 classes. (Contributed by NM, 21-Apr-2001.)
Assertion
Ref Expression
in4

Proof of Theorem in4
StepHypRef Expression
1 in12 3708 . . 3
21ineq2i 3696 . 2
3 inass 3707 . 2
4 inass 3707 . 2
52, 3, 43eqtr4i 2496 1
Colors of variables: wff setvar class
Syntax hints:  =wceq 1395  i^icin 3474
This theorem is referenced by:  inindi  3714  inindir  3715  fh2  26537  disjxpin  27447
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-10 1837  ax-11 1842  ax-12 1854  ax-13 1999  ax-ext 2435
This theorem depends on definitions:  df-bi 185  df-an 371  df-tru 1398  df-ex 1613  df-nf 1617  df-sb 1740  df-clab 2443  df-cleq 2449  df-clel 2452  df-nfc 2607  df-v 3111  df-in 3482
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