Theorem dfiin2 4365

Description: Alternate definition of indexed intersection when is a set. Definition 15(b) of [Suppes] p. 44. (Contributed by NM, 28-Jun-1998.) (Proof shortened by Andrew Salmon, 25-Jul-2011.)

Hypothesis

Ref	Expression
dfiun2.1

Assertion

Ref	Expression
dfiin2

Distinct variable groups:   ,   ,   ,

Proof of Theorem dfiin2

Step	Hyp	Ref	Expression
1		dfiin2g 4363	. 2
2		dfiun2.1	. . 3
3	2	a1i 11	. 2
4	1, 3	mprg 2820	1

Syntax hints:  =wceq 1395  e.wcel 1818  {cab 2442  E.wrex 2808  cvv 3109  |^|cint 4286  |^|_ciin 4331

This theorem is referenced by:  fniinfv  5932  scott0  8325  cfval2  8661  cflim3  8663  cflim2  8664  cfss  8666  hauscmplem  19906  ptbasfi  20082  dihglblem5  37025  dihglb2  37069  intima0  37767

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-rex 2813  df-v 3111  df-int 4287  df-iin 4333