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Mirrors > Home > ILE Home > Th. List > offres | Unicode version |
Description: Pointwise combination commutes with restriction. (Contributed by Stefan O'Rear, 24-Jan-2015.) |
Ref | Expression |
---|---|
offres |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | inss2 3205 |
. . . . . 6
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2 | 1 | sseli 3006 |
. . . . 5
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3 | fvres 5272 |
. . . . . 6
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
4 | fvres 5272 |
. . . . . 6
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
5 | 3, 4 | oveq12d 5607 |
. . . . 5
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6 | 2, 5 | syl 14 |
. . . 4
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7 | 6 | mpteq2ia 3890 |
. . 3
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8 | inindi 3201 |
. . . . 5
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
9 | incom 3176 |
. . . . 5
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
10 | dmres 4689 |
. . . . . 6
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
11 | dmres 4689 |
. . . . . 6
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
12 | 10, 11 | ineq12i 3183 |
. . . . 5
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13 | 8, 9, 12 | 3eqtr4ri 2114 |
. . . 4
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14 | eqid 2083 |
. . . 4
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15 | 13, 14 | mpteq12i 3892 |
. . 3
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16 | resmpt3 4716 |
. . 3
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17 | 7, 15, 16 | 3eqtr4ri 2114 |
. 2
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18 | offval3 5838 |
. . 3
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19 | 18 | reseq1d 4668 |
. 2
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20 | resexg 4707 |
. . 3
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21 | resexg 4707 |
. . 3
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22 | offval3 5838 |
. . 3
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23 | 20, 21, 22 | syl2an 283 |
. 2
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24 | 17, 19, 23 | 3eqtr4a 2141 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 104 ax-ia2 105 ax-ia3 106 ax-in1 577 ax-in2 578 ax-io 663 ax-5 1377 ax-7 1378 ax-gen 1379 ax-ie1 1423 ax-ie2 1424 ax-8 1436 ax-10 1437 ax-11 1438 ax-i12 1439 ax-bndl 1440 ax-4 1441 ax-13 1445 ax-14 1446 ax-17 1460 ax-i9 1464 ax-ial 1468 ax-i5r 1469 ax-ext 2065 ax-coll 3919 ax-sep 3922 ax-pow 3974 ax-pr 3999 ax-un 4223 ax-setind 4315 |
This theorem depends on definitions: df-bi 115 df-3an 922 df-tru 1288 df-fal 1291 df-nf 1391 df-sb 1688 df-eu 1946 df-mo 1947 df-clab 2070 df-cleq 2076 df-clel 2079 df-nfc 2212 df-ne 2250 df-ral 2358 df-rex 2359 df-reu 2360 df-rab 2362 df-v 2614 df-sbc 2827 df-csb 2920 df-dif 2986 df-un 2988 df-in 2990 df-ss 2997 df-pw 3408 df-sn 3428 df-pr 3429 df-op 3431 df-uni 3628 df-iun 3706 df-br 3812 df-opab 3866 df-mpt 3867 df-id 4083 df-xp 4405 df-rel 4406 df-cnv 4407 df-co 4408 df-dm 4409 df-rn 4410 df-res 4411 df-ima 4412 df-iota 4932 df-fun 4969 df-fn 4970 df-f 4971 df-f1 4972 df-fo 4973 df-f1o 4974 df-fv 4975 df-ov 5592 df-oprab 5593 df-mpt2 5594 df-of 5789 |
This theorem is referenced by: (None) |
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