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Theorem dfiin2 3692
 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 3690 . 2
2 dfiun2.1 . . 3
32a1i 9 . 2
41, 3mprg 2378 1
 Colors of variables: wff set class Syntax hints:   wceq 1243   wcel 1393  cab 2026  wrex 2307  cvv 2557  cint 3615  ciin 3658 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-io 630  ax-5 1336  ax-7 1337  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-8 1395  ax-10 1396  ax-11 1397  ax-i12 1398  ax-bndl 1399  ax-4 1400  ax-17 1419  ax-i9 1423  ax-ial 1427  ax-i5r 1428  ax-ext 2022 This theorem depends on definitions:  df-bi 110  df-tru 1246  df-nf 1350  df-sb 1646  df-clab 2027  df-cleq 2033  df-clel 2036  df-nfc 2167  df-ral 2311  df-rex 2312  df-v 2559  df-int 3616  df-iin 3660 This theorem is referenced by: (None)
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