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Theorem fint 5622
 Description: Function into an intersection. (Contributed by NM, 14-Oct-1999.) (Proof shortened by Andrew Salmon, 17-Sep-2011.)
Hypothesis
Ref Expression
fint.1
Assertion
Ref Expression
fint
Distinct variable groups:   ,   ,   ,

Proof of Theorem fint
StepHypRef Expression
1 ssint 4066 . . . 4
21anbi2i 676 . . 3
3 fint.1 . . . 4
4 r19.28zv 3723 . . . 4
53, 4ax-mp 8 . . 3
62, 5bitr4i 244 . 2
7 df-f 5458 . 2
8 df-f 5458 . . 3
98ralbii 2729 . 2
106, 7, 93bitr4i 269 1
 Colors of variables: wff set class Syntax hints:   wb 177   wa 359   wne 2599  wral 2705   wss 3320  c0 3628  cint 4050   crn 4879   wfn 5449  wf 5450 This theorem is referenced by:  chintcli  22833 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 2417 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 2423  df-cleq 2429  df-clel 2432  df-nfc 2561  df-ne 2601  df-ral 2710  df-v 2958  df-dif 3323  df-in 3327  df-ss 3334  df-nul 3629  df-int 4051  df-f 5458
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