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Theorem fintm 5018
Description: Function into an intersection. (Contributed by Jim Kingdon, 28-Dec-2018.)
Hypothesis
Ref Expression
fintm.1
Assertion
Ref Expression
fintm  F : --> |^|  F : -->
Distinct variable groups:   ,   ,   , F

Proof of Theorem fintm
StepHypRef Expression
1 ssint 3622 . . . 4  ran 
F  C_  |^|  ran  F  C_
21anbi2i 430 . . 3  F  Fn  ran  F  C_  |^|  F  Fn  ran  F  C_
3 fintm.1 . . . 4
4 r19.28mv 3308 . . . 4  F  Fn  ran  F  C_  F  Fn  ran  F  C_
53, 4ax-mp 7 . . 3  F  Fn  ran  F  C_  F  Fn  ran  F  C_
62, 5bitr4i 176 . 2  F  Fn  ran  F  C_  |^|  F  Fn  ran  F  C_
7 df-f 4849 . 2  F : --> |^|  F  Fn  ran  F  C_  |^|
8 df-f 4849 . . 3  F : -->  F  Fn  ran  F 
C_
98ralbii 2324 . 2  F : -->  F  Fn  ran  F  C_
106, 7, 93bitr4i 201 1  F : --> |^|  F : -->
Colors of variables: wff set class
Syntax hints:   wa 97   wb 98  wex 1378   wcel 1390  wral 2300    C_ wss 2911   |^|cint 3606   ran crn 4289    Fn wfn 4840   -->wf 4841
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 629  ax-5 1333  ax-7 1334  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-8 1392  ax-10 1393  ax-11 1394  ax-i12 1395  ax-bnd 1396  ax-4 1397  ax-17 1416  ax-i9 1420  ax-ial 1424  ax-i5r 1425  ax-ext 2019
This theorem depends on definitions:  df-bi 110  df-tru 1245  df-nf 1347  df-sb 1643  df-clab 2024  df-cleq 2030  df-clel 2033  df-nfc 2164  df-ral 2305  df-v 2553  df-in 2918  df-ss 2925  df-int 3607  df-f 4849
This theorem is referenced by: (None)
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