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Mirrors > Home > ILE Home > Th. List > fvco3 | Unicode version |
Description: Value of a function composition. (Contributed by NM, 3-Jan-2004.) (Revised by Mario Carneiro, 26-Dec-2014.) |
Ref | Expression |
---|---|
fvco3 |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ffn 5364 |
. 2
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2 | fvco2 5584 |
. 2
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3 | 1, 2 | sylan 283 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 106 ax-ia2 107 ax-ia3 108 ax-io 709 ax-5 1447 ax-7 1448 ax-gen 1449 ax-ie1 1493 ax-ie2 1494 ax-8 1504 ax-10 1505 ax-11 1506 ax-i12 1507 ax-bndl 1509 ax-4 1510 ax-17 1526 ax-i9 1530 ax-ial 1534 ax-i5r 1535 ax-14 2151 ax-ext 2159 ax-sep 4120 ax-pow 4173 ax-pr 4208 |
This theorem depends on definitions: df-bi 117 df-3an 980 df-tru 1356 df-nf 1461 df-sb 1763 df-eu 2029 df-mo 2030 df-clab 2164 df-cleq 2170 df-clel 2173 df-nfc 2308 df-ral 2460 df-rex 2461 df-v 2739 df-sbc 2963 df-un 3133 df-in 3135 df-ss 3142 df-pw 3577 df-sn 3598 df-pr 3599 df-op 3601 df-uni 3810 df-br 4003 df-opab 4064 df-id 4292 df-xp 4631 df-rel 4632 df-cnv 4633 df-co 4634 df-dm 4635 df-rn 4636 df-res 4637 df-ima 4638 df-iota 5177 df-fun 5217 df-fn 5218 df-f 5219 df-fv 5223 |
This theorem is referenced by: fvco4 5587 foco2 5752 f1ocnvfv1 5775 f1ocnvfv2 5776 fcof1 5781 fcofo 5782 cocan1 5785 cocan2 5786 isotr 5814 algrflem 6227 algrflemg 6228 difinfsn 7096 ctssdccl 7107 cc3 7264 0tonninf 10434 1tonninf 10435 summodclem3 11381 fsumf1o 11391 fsumcl2lem 11399 fsumadd 11407 fsummulc2 11449 prodmodclem3 11576 fprodf1o 11589 fprodmul 11592 algcvg 12040 eulerthlemth 12224 ennnfonelemnn0 12415 ctinfomlemom 12420 mhmco 12806 cnptopco 13593 lmtopcnp 13621 upxp 13643 uptx 13645 cnmpt11 13654 cnmpt21 13662 comet 13870 cnmetdval 13900 climcncf 13942 cncfco 13949 limccnpcntop 14015 dvcoapbr 14042 dvcjbr 14043 dvfre 14045 isomninnlem 14638 iswomninnlem 14657 ismkvnnlem 14660 |
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