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replace codomain by codomain/range for onto functions
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as remarked by JK
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avekens committed Jan 5, 2025
1 parent 36cd995 commit 49572f0
Showing 1 changed file with 4 additions and 4 deletions.
8 changes: 4 additions & 4 deletions set.mm
Original file line number Diff line number Diff line change
Expand Up @@ -64074,8 +64074,8 @@ empty set when it is not meaningful (as shown by ~ ndmfv and ~ fvprc ).
CKUFUDTAUCCLMNOPABCRBAUARS $.

$( A relation is a one-to-one onto function iff its converse is a one-to-one
onto function with domain and codomain interchanged. (Contributed by NM,
8-Dec-2003.) $)
onto function with domain and codomain/range interchanged. (Contributed
by NM, 8-Dec-2003.) $)
f1ocnvb $p |- ( Rel F ->
( F : A -1-1-onto-> B <-> `' F : B -1-1-onto-> A ) ) $=
( wrel wf1o ccnv f1ocnv wceq wb dfrel2 f1oeq1 sylbi syl5ib impbid2 ) CDZABC
Expand Down Expand Up @@ -76850,8 +76850,8 @@ as a separate axiom in an axiom system (such as Kunen's) that uses this
ex focdmex syl6ci imp ) ABDEZBCFZAGFZUDUEDHZGFZUGADIZJZUFUDUEUHUDUGBKUEUHUD
ABDABDLMUGBCNOTUDUGAUIPUJABDQUGAUIRSUGAGUIUAUBUC $.

$( The codomain of a 1-1 onto function is a set iff its domain is a set.
(Contributed by AV, 21-Mar-2019.) $)
$( The codomain/range of a 1-1 onto function is a set iff its domain is a
set. (Contributed by AV, 21-Mar-2019.) $)
f1ovv $p |- ( F : A -1-1-onto-> B -> ( A e. _V <-> B e. _V ) ) $=
( wf1o cvv wcel wfo f1ofo focdmex syl5com wf1 wi f1of1 f1dmex ex syl impbid
) ABCDZAEFZBEFZRABCGSTABCHABECIJRABCKZTSLABCMUATSABECNOPQ $.
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