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Mirrors > Home > MPE Home > Th. List > fnfvrnss | Structured version Visualization version Unicode version |
Description: An upper bound for range determined by function values. (Contributed by NM, 8-Oct-2004.) |
Ref | Expression |
---|---|
fnfvrnss |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ffnfv 6388 | . 2 | |
2 | frn 6053 | . 2 | |
3 | 1, 2 | sylbir 225 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wi 4 wa 384 wcel 1990 wral 2912 wss 3574 crn 5115 wfn 5883 wf 5884 cfv 5888 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1722 ax-4 1737 ax-5 1839 ax-6 1888 ax-7 1935 ax-9 1999 ax-10 2019 ax-11 2034 ax-12 2047 ax-13 2246 ax-ext 2602 ax-sep 4781 ax-nul 4789 ax-pr 4906 |
This theorem depends on definitions: df-bi 197 df-or 385 df-an 386 df-3an 1039 df-tru 1486 df-ex 1705 df-nf 1710 df-sb 1881 df-eu 2474 df-mo 2475 df-clab 2609 df-cleq 2615 df-clel 2618 df-nfc 2753 df-ral 2917 df-rex 2918 df-rab 2921 df-v 3202 df-sbc 3436 df-dif 3577 df-un 3579 df-in 3581 df-ss 3588 df-nul 3916 df-if 4087 df-sn 4178 df-pr 4180 df-op 4184 df-uni 4437 df-br 4654 df-opab 4713 df-mpt 4730 df-id 5024 df-xp 5120 df-rel 5121 df-cnv 5122 df-co 5123 df-dm 5124 df-rn 5125 df-iota 5851 df-fun 5890 df-fn 5891 df-f 5892 df-fv 5896 |
This theorem is referenced by: ffvresb 6394 dffi3 8337 infxpenlem 8836 alephsing 9098 srgfcl 18515 mplind 19502 1stckgenlem 21356 psmetxrge0 22118 plyreres 24038 aannenlem1 24083 subuhgr 26178 subupgr 26179 subumgr 26180 subusgr 26181 rmulccn 29974 esumfsup 30132 sxbrsigalem3 30334 sitgf 30409 dihf11lem 36555 hdmaprnN 37156 hgmaprnN 37193 ntrrn 38420 volicoff 40212 dirkercncflem2 40321 fourierdlem15 40339 fourierdlem42 40366 |
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