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Mirrors > Home > MPE Home > Th. List > fvco | Structured version Visualization version Unicode version |
Description: Value of a function composition. Similar to Exercise 5 of [TakeutiZaring] p. 28. (Contributed by NM, 22-Apr-2006.) (Proof shortened by Mario Carneiro, 26-Dec-2014.) |
Ref | Expression |
---|---|
fvco |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | funfn 5918 | . 2 | |
2 | fvco2 6273 | . 2 | |
3 | 1, 2 | sylanb 489 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wi 4 wa 384 wceq 1483 wcel 1990 cdm 5114 ccom 5118 wfun 5882 wfn 5883 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-8 1992 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-pow 4843 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-ne 2795 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-id 5024 df-xp 5120 df-rel 5121 df-cnv 5122 df-co 5123 df-dm 5124 df-rn 5125 df-res 5126 df-ima 5127 df-iota 5851 df-fun 5890 df-fn 5891 df-fv 5896 |
This theorem is referenced by: fin23lem30 9164 hashkf 13119 hashgval 13120 gsumpropd2lem 17273 ofco2 20257 opfv 29448 xppreima 29449 psgnfzto1stlem 29850 smatlem 29863 mdetpmtr1 29889 madjusmdetlem2 29894 madjusmdetlem4 29896 eulerpartlemgvv 30438 eulerpartlemgu 30439 sseqfv2 30456 reprpmtf1o 30704 hgt750lemg 30732 comptiunov2i 37998 choicefi 39392 fvcod 39423 evthiccabs 39718 cncficcgt0 40101 dvsinax 40127 fvvolioof 40206 fvvolicof 40208 stirlinglem14 40304 fourierdlem42 40366 hoicvr 40762 hoi2toco 40821 ovolval3 40861 ovolval4lem1 40863 ovnovollem1 40870 ovnovollem2 40871 |
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