Theorem in32 3709

Description: A rearrangement of intersection. (Contributed by NM, 21-Apr-2001.) (Proof shortened by Andrew Salmon, 26-Jun-2011.)

Assertion

Ref	Expression
in32

Proof of Theorem in32

Step	Hyp	Ref	Expression
1		inass 3707	. 2
2		in12 3708	. 2
3		incom 3690	. 2
4	1, 2, 3	3eqtri 2490	1

Syntax hints:  =wceq 1395  i^icin 3474

This theorem is referenced by:  in13  3710  inrot  3712  wefrc  4878  imainrect  5453  fpwwe2  9042  incexclem  13648  ressress  14694  kgeni  20038  kgencn3  20059  fclsrest  20525  voliunlem1  21960  sspred  29252

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