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Theorem dfiin2 4002
 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:   ,   ,   ,
Allowed substitution hints:   ()   ()

Proof of Theorem dfiin2
StepHypRef Expression
1 dfiin2g 4000 . 2
2 dfiun2.1 . . 3
32a1i 10 . 2
41, 3mprg 2683 1
 Colors of variables: wff setvar class Syntax hints:   wceq 1642   wcel 1710  cab 2339  wrex 2615  cvv 2859  cint 3926  ciin 3970 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-7 1734  ax-11 1746  ax-12 1925  ax-ext 2334 This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649  df-clab 2340  df-cleq 2346  df-clel 2349  df-nfc 2478  df-ral 2619  df-rex 2620  df-v 2861  df-int 3927  df-iin 3972 This theorem is referenced by:  fniinfv  5372
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