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Mathbox for Norm Megill |
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Mirrors > Home > MPE Home > Th. List > Mathboxes > cdlemg41 | Structured version Unicode version |
Description: Convert cdlemg40 34669 to function composition. TODO: Fix comment. (Contributed by NM, 31-May-2013.) |
Ref | Expression |
---|---|
cdlemg35.l |
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
cdlemg35.j |
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
cdlemg35.m |
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
cdlemg35.a |
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
cdlemg35.h |
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
cdlemg35.t |
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Ref | Expression |
---|---|
cdlemg41 |
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | cdlemg35.l |
. . 3
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
2 | cdlemg35.j |
. . 3
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
3 | cdlemg35.m |
. . 3
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
4 | cdlemg35.a |
. . 3
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
5 | cdlemg35.h |
. . 3
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
6 | cdlemg35.t |
. . 3
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
7 | 1, 2, 3, 4, 5, 6 | cdlemg40 34669 |
. 2
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
8 | simp1 988 |
. . . . 5
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9 | simp3 990 |
. . . . 5
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
10 | simp2ll 1055 |
. . . . 5
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11 | 1, 4, 5, 6 | ltrncoval 34097 |
. . . . 5
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12 | 8, 9, 10, 11 | syl3anc 1219 |
. . . 4
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13 | 12 | oveq2d 6208 |
. . 3
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14 | 13 | oveq1d 6207 |
. 2
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
15 | simp2rl 1057 |
. . . . 5
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
16 | 1, 4, 5, 6 | ltrncoval 34097 |
. . . . 5
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17 | 8, 9, 15, 16 | syl3anc 1219 |
. . . 4
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18 | 17 | oveq2d 6208 |
. . 3
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19 | 18 | oveq1d 6207 |
. 2
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20 | 7, 14, 19 | 3eqtr4d 2502 |
1
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Colors of variables: wff setvar class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1592 ax-4 1603 ax-5 1671 ax-6 1710 ax-7 1730 ax-8 1760 ax-9 1762 ax-10 1777 ax-11 1782 ax-12 1794 ax-13 1952 ax-ext 2430 ax-rep 4503 ax-sep 4513 ax-nul 4521 ax-pow 4570 ax-pr 4631 ax-un 6474 ax-riotaBAD 32912 |
This theorem depends on definitions: df-bi 185 df-or 370 df-an 371 df-3or 966 df-3an 967 df-tru 1373 df-ex 1588 df-nf 1591 df-sb 1703 df-eu 2264 df-mo 2265 df-clab 2437 df-cleq 2443 df-clel 2446 df-nfc 2601 df-ne 2646 df-nel 2647 df-ral 2800 df-rex 2801 df-reu 2802 df-rmo 2803 df-rab 2804 df-v 3072 df-sbc 3287 df-csb 3389 df-dif 3431 df-un 3433 df-in 3435 df-ss 3442 df-nul 3738 df-if 3892 df-pw 3962 df-sn 3978 df-pr 3980 df-op 3984 df-uni 4192 df-iun 4273 df-iin 4274 df-br 4393 df-opab 4451 df-mpt 4452 df-id 4736 df-xp 4946 df-rel 4947 df-cnv 4948 df-co 4949 df-dm 4950 df-rn 4951 df-res 4952 df-ima 4953 df-iota 5481 df-fun 5520 df-fn 5521 df-f 5522 df-f1 5523 df-fo 5524 df-f1o 5525 df-fv 5526 df-riota 6153 df-ov 6195 df-oprab 6196 df-mpt2 6197 df-1st 6679 df-2nd 6680 df-undef 6894 df-map 7318 df-poset 15220 df-plt 15232 df-lub 15248 df-glb 15249 df-join 15250 df-meet 15251 df-p0 15313 df-p1 15314 df-lat 15320 df-clat 15382 df-oposet 33129 df-ol 33131 df-oml 33132 df-covers 33219 df-ats 33220 df-atl 33251 df-cvlat 33275 df-hlat 33304 df-llines 33450 df-lplanes 33451 df-lvols 33452 df-lines 33453 df-psubsp 33455 df-pmap 33456 df-padd 33748 df-lhyp 33940 df-laut 33941 df-ldil 34056 df-ltrn 34057 df-trl 34111 |
This theorem is referenced by: ltrnco 34671 |
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