Theorem indif2 3740

Description: Bring an intersection in and out of a class difference. (Contributed by Jeff Hankins, 15-Jul-2009.)

Assertion

Ref	Expression
indif2

Proof of Theorem indif2

Step	Hyp	Ref	Expression
1		inass 3707	. 2
2		invdif 3738	. 2
3		invdif 3738	. . 3
4	3	ineq2i 3696	. 2
5	1, 2, 4	3eqtr3ri 2495	1

Syntax hints:  =wceq 1395  cvv 3109  \cdif 3472  i^icin 3474

This theorem is referenced by:  indif1  3741  indifcom  3742  marypha1lem  7913  difopn  19535  restcld  19673  difmbl  21953  voliunlem1  21960  imadifxp  27458  wfi  29287  frind  29323  mblfinlem3  30053  mblfinlem4  30054  topbnd  30142

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-ral 2812  df-rab 2816  df-v 3111  df-dif 3478  df-in 3482