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Mirrors > Home > MPE Home > Th. List > funforn | Structured version Visualization version GIF version |
Description: A function maps its domain onto its range. (Contributed by NM, 23-Jul-2004.) |
Ref | Expression |
---|---|
funforn | β’ (Fun π΄ β π΄:dom π΄βontoβran π΄) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | funfn 6532 | . 2 β’ (Fun π΄ β π΄ Fn dom π΄) | |
2 | dffn4 6763 | . 2 β’ (π΄ Fn dom π΄ β π΄:dom π΄βontoβran π΄) | |
3 | 1, 2 | bitri 275 | 1 β’ (Fun π΄ β π΄:dom π΄βontoβran π΄) |
Colors of variables: wff setvar class |
Syntax hints: β wb 205 dom cdm 5634 ran crn 5635 Fun wfun 6491 Fn wfn 6492 βontoβwfo 6495 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1798 ax-4 1812 ax-5 1914 ax-6 1972 ax-7 2012 ax-9 2117 ax-ext 2708 |
This theorem depends on definitions: df-bi 206 df-an 398 df-ex 1783 df-cleq 2729 df-fn 6500 df-fo 6503 |
This theorem is referenced by: fimacnvinrn 7023 imacosupp 8141 ordtypelem8 9462 wdomima2g 9523 imadomg 10471 gruima 10739 oppglsm 19425 1stcrestlem 22806 dfac14 22972 qtoptop2 23053 fsupprnfi 31610 rn1st 43509 |
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