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Theorem rnmptss 6060
Description: The range of an operation given by the "maps to" notation as a subset. (Contributed by Thierry Arnoux, 24-Sep-2017.)
Hypothesis
Ref Expression
rnmptss.1
Assertion
Ref Expression
rnmptss
Distinct variable groups:   ,   ,

Proof of Theorem rnmptss
StepHypRef Expression
1 rnmptss.1 . . 3
21fmpt 6052 . 2
3 frn 5742 . 2
42, 3sylbi 195 1
Colors of variables: wff setvar class
Syntax hints:  ->wi 4  =wceq 1395  e.wcel 1818  A.wral 2807  C_wss 3475  e.cmpt 4510  rancrn 5005  -->wf 5589
This theorem is referenced by:  iunon  7028  iinon  7030  gruiun  9198  smadiadetlem3lem2  19169  tgiun  19481  ustuqtop0  20743  metustssOLD  21056  metustss  21057  efabl  22937  efsubm  22938  gsummpt2co  27771  locfinreflem  27843  gsumesum  28067  esumlub  28068  sxbrsigalem0  28242  omsmon  28267  suprnmpt  31451  fourierdlem31  31920  fourierdlem53  31942  fourierdlem111  32000
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-9 1822  ax-10 1837  ax-11 1842  ax-12 1854  ax-13 1999  ax-ext 2435  ax-sep 4573  ax-nul 4581  ax-pr 4691
This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-3an 975  df-tru 1398  df-ex 1613  df-nf 1617  df-sb 1740  df-eu 2286  df-mo 2287  df-clab 2443  df-cleq 2449  df-clel 2452  df-nfc 2607  df-ne 2654  df-ral 2812  df-rex 2813  df-rab 2816  df-v 3111  df-sbc 3328  df-dif 3478  df-un 3480  df-in 3482  df-ss 3489  df-nul 3785  df-if 3942  df-sn 4030  df-pr 4032  df-op 4036  df-uni 4250  df-br 4453  df-opab 4511  df-mpt 4512  df-id 4800  df-xp 5010  df-rel 5011  df-cnv 5012  df-co 5013  df-dm 5014  df-rn 5015  df-res 5016  df-ima 5017  df-iota 5556  df-fun 5595  df-fn 5596  df-f 5597  df-fv 5601
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