Theorem in12 3708

Description: A rearrangement of intersection. (Contributed by NM, 21-Apr-2001.)

Assertion

Ref	Expression
in12

Proof of Theorem in12

Step	Hyp	Ref	Expression
1		incom 3690	. . 3
2	1	ineq1i 3695	. 2
3		inass 3707	. 2
4		inass 3707	. 2
5	2, 3, 4	3eqtr3i 2494	1

Syntax hints:  =wceq 1395  i^icin 3474

This theorem is referenced by:  in32  3709  in31  3711  in4  3713  resdmres  5503  kmlem12  8562  ressress  14694  fh1  26536  fh2  26537  mdslmd3i  27251

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