Theorem iinconst 4340

Description: Indexed intersection of a constant class, i.e. where does not depend on . (Contributed by Mario Carneiro, 6-Feb-2015.)

Assertion

Ref	Expression
iinconst

Distinct variable groups:   ,   ,

Proof of Theorem iinconst

Dummy variable is distinct from all other variables.

Step	Hyp	Ref	Expression
1		r19.3rzv 3922	. . 3
2		vex 3112	. . . 4
3		eliin 4336	. . . 4
4	2, 3	ax-mp 5	. . 3
5	1, 4	syl6rbbr 264	. 2
6	5	eqrdv 2454	1

Syntax hints:  ->wi 4  <->wb 184  =wceq 1395  e.wcel 1818  =/=wne 2652  A.wral 2807  cvv 3109  c0 3784  |^|_ciin 4331

This theorem is referenced by:  iin0  4626  ptbasfi  20082

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-or 370  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-ne 2654  df-ral 2812  df-v 3111  df-dif 3478  df-nul 3785  df-iin 4333