Theorem iinss1 4343

Description: Subclass theorem for indexed intersection. (Contributed by NM, 24-Jan-2012.)

Assertion

Ref	Expression
iinss1

Distinct variable groups:   ,   ,

Proof of Theorem iinss1

Dummy variable is distinct from all other variables.

Step	Hyp	Ref	Expression
1		ssralv 3563	. . 3
2		vex 3112	. . . 4
3		eliin 4336	. . . 4
4	2, 3	ax-mp 5	. . 3
5		eliin 4336	. . . 4
6	2, 5	ax-mp 5	. . 3
7	1, 4, 6	3imtr4g 270	. 2
8	7	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:  polcon3N  35641

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