Theorem iinss2 4382

Description: An indexed intersection is included in any of its members. (Contributed by FL, 15-Oct-2012.)

Assertion

Ref	Expression
iinss2

Proof of Theorem iinss2

Dummy variable is distinct from all other variables.

Step	Hyp	Ref	Expression
1		vex 3112	. . . . 5
2		eliin 4336	. . . . 5
3	1, 2	ax-mp 5	. . . 4
4		rsp 2823	. . . 4
5	3, 4	sylbi 195	. . 3
6	5	com12 31	. 2
7	6	ssrdv 3509	1

Syntax hints:  ->wi 4  <->wb 184  e.wcel 1818  A.wral 2807  cvv 3109  C_wss 3475  |^|_ciin 4331

This theorem is referenced by:  dmiin  5251  gruiin  9209  txtube  20141

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-v 3111  df-in 3482  df-ss 3489  df-iin 4333