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Mirrors > Home > MPE Home > Th. List > fnfco | Structured version Visualization version Unicode version |
Description: Composition of two functions. (Contributed by NM, 22-May-2006.) |
Ref | Expression |
---|---|
fnfco |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-f 5892 | . 2 | |
2 | fnco 5999 | . . 3 | |
3 | 2 | 3expb 1266 | . 2 |
4 | 1, 3 | sylan2b 492 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wi 4 wa 384 wss 3574 crn 5115 ccom 5118 wfn 5883 wf 5884 |
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-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-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-fun 5890 df-fn 5891 df-f 5892 |
This theorem is referenced by: cocan1 6546 cocan2 6547 ofco 6917 1stcof 7196 2ndcof 7197 axcc3 9260 dmaf 16699 cdaf 16700 gsumzaddlem 18321 prdstopn 21431 xpstopnlem2 21614 prdstgpd 21928 prdsxmslem2 22334 uniiccdif 23346 uniiccvol 23348 uniioombllem2 23351 resinf1o 24282 jensen 24715 occllem 28162 nlelchi 28920 hmopidmchi 29010 iprodefisumlem 31626 brcoffn 38328 brcofffn 38329 stoweidlem27 40244 |
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