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Mirrors > Home > ILE Home > Th. List > topnvalg | Unicode version |
Description: Value of the topology extractor function. (Contributed by Mario Carneiro, 13-Aug-2015.) (Revised by Jim Kingdon, 11-Feb-2023.) |
Ref | Expression |
---|---|
topnval.1 |
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topnval.2 |
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Ref | Expression |
---|---|
topnvalg |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | elex 2644 |
. . 3
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2 | restfn 11808 |
. . . 4
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3 | topnval.2 |
. . . . 5
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4 | tsetslid 11793 |
. . . . . 6
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5 | 4 | slotex 11670 |
. . . . 5
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6 | 3, 5 | syl5eqel 2181 |
. . . 4
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7 | topnval.1 |
. . . . 5
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8 | baseslid 11699 |
. . . . . 6
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9 | 8 | slotex 11670 |
. . . . 5
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10 | 7, 9 | syl5eqel 2181 |
. . . 4
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11 | fnovex 5720 |
. . . 4
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12 | 2, 6, 10, 11 | mp3an2i 1285 |
. . 3
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13 | fveq2 5340 |
. . . . . 6
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14 | 13, 3 | syl6eqr 2145 |
. . . . 5
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15 | fveq2 5340 |
. . . . . 6
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16 | 15, 7 | syl6eqr 2145 |
. . . . 5
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17 | 14, 16 | oveq12d 5708 |
. . . 4
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18 | df-topn 11807 |
. . . 4
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19 | 17, 18 | fvmptg 5415 |
. . 3
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20 | 1, 12, 19 | syl2anc 404 |
. 2
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21 | 20 | eqcomd 2100 |
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 105 ax-ia2 106 ax-ia3 107 ax-io 668 ax-5 1388 ax-7 1389 ax-gen 1390 ax-ie1 1434 ax-ie2 1435 ax-8 1447 ax-10 1448 ax-11 1449 ax-i12 1450 ax-bndl 1451 ax-4 1452 ax-13 1456 ax-14 1457 ax-17 1471 ax-i9 1475 ax-ial 1479 ax-i5r 1480 ax-ext 2077 ax-coll 3975 ax-sep 3978 ax-pow 4030 ax-pr 4060 ax-un 4284 ax-cnex 7533 ax-resscn 7534 ax-1re 7536 ax-addrcl 7539 |
This theorem depends on definitions: df-bi 116 df-3an 929 df-tru 1299 df-nf 1402 df-sb 1700 df-eu 1958 df-mo 1959 df-clab 2082 df-cleq 2088 df-clel 2091 df-nfc 2224 df-ral 2375 df-rex 2376 df-reu 2377 df-rab 2379 df-v 2635 df-sbc 2855 df-csb 2948 df-un 3017 df-in 3019 df-ss 3026 df-pw 3451 df-sn 3472 df-pr 3473 df-op 3475 df-uni 3676 df-int 3711 df-iun 3754 df-br 3868 df-opab 3922 df-mpt 3923 df-id 4144 df-xp 4473 df-rel 4474 df-cnv 4475 df-co 4476 df-dm 4477 df-rn 4478 df-res 4479 df-ima 4480 df-iota 5014 df-fun 5051 df-fn 5052 df-f 5053 df-f1 5054 df-fo 5055 df-f1o 5056 df-fv 5057 df-ov 5693 df-oprab 5694 df-mpt2 5695 df-1st 5949 df-2nd 5950 df-inn 8521 df-2 8579 df-3 8580 df-4 8581 df-5 8582 df-6 8583 df-7 8584 df-8 8585 df-9 8586 df-ndx 11646 df-slot 11647 df-base 11649 df-tset 11724 df-rest 11806 df-topn 11807 |
This theorem is referenced by: topnidg 11817 topnpropgd 11818 |
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