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Theorem dfiin2 4118
 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 4116 . 2
2 dfiun2.1 . . 3
32a1i 11 . 2
41, 3mprg 2767 1
 Colors of variables: wff set class Syntax hints:   wceq 1652   wcel 1725  cab 2421  wrex 2698  cvv 2948  cint 4042  ciin 4086 This theorem is referenced by:  fniinfv  5776  scott0  7799  cfval2  8129  cflim3  8131  cflim2  8132  cfss  8134  hauscmplem  17457  ptbasfi  17601  dihglblem5  31935  dihglb2  31979 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2416 This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-clab 2422  df-cleq 2428  df-clel 2431  df-nfc 2560  df-ral 2702  df-rex 2703  df-v 2950  df-int 4043  df-iin 4088
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