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Mirrors > Home > MPE Home > Th. List > ffrn | Structured version Visualization version GIF version |
Description: A function maps to its range. (Contributed by Glauco Siliprandi, 3-Mar-2021.) |
Ref | Expression |
---|---|
ffrn | โข (๐น:๐ดโถ๐ต โ ๐น:๐ดโถran ๐น) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ffn 6669 | . 2 โข (๐น:๐ดโถ๐ต โ ๐น Fn ๐ด) | |
2 | dffn3 6682 | . 2 โข (๐น Fn ๐ด โ ๐น:๐ดโถran ๐น) | |
3 | 1, 2 | sylib 217 | 1 โข (๐น:๐ดโถ๐ต โ ๐น:๐ดโถran ๐น) |
Colors of variables: wff setvar class |
Syntax hints: โ wi 4 ran crn 5635 Fn wfn 6492 โถwf 6493 |
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-8 2109 ax-9 2117 ax-ext 2704 |
This theorem depends on definitions: df-bi 206 df-an 398 df-tru 1545 df-ex 1783 df-sb 2069 df-clab 2711 df-cleq 2725 df-clel 2811 df-v 3446 df-in 3918 df-ss 3928 df-f 6501 |
This theorem is referenced by: fo2ndf 8054 mapsnd 8827 itg1val2 25064 volicoff 44322 f1cof1b 45395 f1ocof1ob 45399 fundcmpsurbijinjpreimafv 45685 |
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