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Theorem fin 5770
 Description: Mapping into an intersection. (Contributed by NM, 14-Sep-1999.) (Proof shortened by Andrew Salmon, 17-Sep-2011.)
Assertion
Ref Expression
fin

Proof of Theorem fin
StepHypRef Expression
1 ssin 3719 . . . 4
21anbi2i 694 . . 3
3 anandi 828 . . 3
42, 3bitr3i 251 . 2
5 df-f 5597 . 2
6 df-f 5597 . . 3
7 df-f 5597 . . 3
86, 7anbi12i 697 . 2
94, 5, 83bitr4i 277 1
 Colors of variables: wff setvar class Syntax hints:  <->wb 184  /\wa 369  i^icin 3474  C_wss 3475  rancrn 5005  Fnwfn 5588  -->wf 5589 This theorem is referenced by:  maprnin  27554 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-v 3111  df-in 3482  df-ss 3489  df-f 5597
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