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Theorem dfiin2 3912
 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 3910 . 2
2 dfiun2.1 . . 3
32a1i 12 . 2
41, 3mprg 2587 1
 Colors of variables: wff set class Syntax hints:   wceq 1619   wcel 1621  cab 2244  wrex 2519  cvv 2763  cint 3836  ciin 3880 This theorem is referenced by:  fniinfv  5515  scott0  7524  cfval2  7854  cflim3  7856  cflim2  7857  cfss  7859  hauscmplem  17095  ptbasfi  17238  dihglblem5  30655  dihglb2  30699 This theorem was proved from axioms:  ax-1 7  ax-2 8  ax-3 9  ax-mp 10  ax-5 1533  ax-6 1534  ax-7 1535  ax-gen 1536  ax-8 1623  ax-11 1624  ax-17 1628  ax-12o 1664  ax-10 1678  ax-9 1684  ax-4 1692  ax-16 1927  ax-ext 2239 This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-tru 1315  df-ex 1538  df-nf 1540  df-sb 1884  df-clab 2245  df-cleq 2251  df-clel 2254  df-nfc 2383  df-ral 2523  df-rex 2524  df-v 2765  df-int 3837  df-iin 3882
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