Theorem indifcom 3742

Description: Commutation law for intersection and difference. (Contributed by Scott Fenton, 18-Feb-2013.)

Assertion

Ref	Expression
indifcom

Proof of Theorem indifcom

Step	Hyp	Ref	Expression
1		incom 3690	. . 3
2	1	difeq1i 3617	. 2
3		indif2 3740	. 2
4		indif2 3740	. 2
5	2, 3, 4	3eqtr4i 2496	1

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

This theorem is referenced by:  dfsup3OLD  7924  ufprim  20410  cmmbl  21945  unmbl  21948  volinun  21956  limciun  22298

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