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Theorem fin 5355
 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 3329 . . . 4
21anbi2i 453 . . 3
3 anandi 580 . . 3
42, 3bitr3i 185 . 2
5 df-f 5173 . 2
6 df-f 5173 . . 3
7 df-f 5173 . . 3
86, 7anbi12i 456 . 2
94, 5, 83bitr4i 211 1
 Colors of variables: wff set class Syntax hints:   wa 103   wb 104   cin 3101   wss 3102   crn 4586   wfn 5164  wf 5165 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 699  ax-5 1427  ax-7 1428  ax-gen 1429  ax-ie1 1473  ax-ie2 1474  ax-8 1484  ax-10 1485  ax-11 1486  ax-i12 1487  ax-bndl 1489  ax-4 1490  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-i5r 1515  ax-ext 2139 This theorem depends on definitions:  df-bi 116  df-tru 1338  df-nf 1441  df-sb 1743  df-clab 2144  df-cleq 2150  df-clel 2153  df-nfc 2288  df-v 2714  df-in 3108  df-ss 3115  df-f 5173 This theorem is referenced by: (None)
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