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Mirrors > Home > ILE Home > Th. List > inftonninf | Unicode version |
Description: The mapping of ![]() |
Ref | Expression |
---|---|
fxnn0nninf.g |
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fxnn0nninf.f |
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fxnn0nninf.i |
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Ref | Expression |
---|---|
inftonninf |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | fxnn0nninf.i |
. . 3
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2 | 1 | fveq1i 5376 |
. 2
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3 | pnf0xnn0 8951 |
. . 3
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4 | omex 4467 |
. . . 4
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5 | 1oex 6275 |
. . . . 5
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6 | 5 | snex 4069 |
. . . 4
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7 | 4, 6 | xpex 4614 |
. . 3
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8 | pnfnre 7731 |
. . . . . 6
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9 | 8 | neli 2379 |
. . . . 5
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10 | nn0re 8890 |
. . . . 5
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11 | 9, 10 | mto 634 |
. . . 4
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12 | fxnn0nninf.g |
. . . . . . 7
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13 | fxnn0nninf.f |
. . . . . . 7
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14 | 12, 13 | fnn0nninf 10103 |
. . . . . 6
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15 | 14 | fdmi 5238 |
. . . . 5
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16 | 15 | eleq2i 2181 |
. . . 4
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17 | 11, 16 | mtbir 643 |
. . 3
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18 | fsnunfv 5575 |
. . 3
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19 | 3, 7, 17, 18 | mp3an 1298 |
. 2
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20 | fconstmpt 4546 |
. 2
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21 | 2, 19, 20 | 3eqtri 2139 |
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-in1 586 ax-in2 587 ax-io 681 ax-5 1406 ax-7 1407 ax-gen 1408 ax-ie1 1452 ax-ie2 1453 ax-8 1465 ax-10 1466 ax-11 1467 ax-i12 1468 ax-bndl 1469 ax-4 1470 ax-13 1474 ax-14 1475 ax-17 1489 ax-i9 1493 ax-ial 1497 ax-i5r 1498 ax-ext 2097 ax-coll 4003 ax-sep 4006 ax-nul 4014 ax-pow 4058 ax-pr 4091 ax-un 4315 ax-setind 4412 ax-iinf 4462 ax-cnex 7636 ax-resscn 7637 ax-1cn 7638 ax-1re 7639 ax-icn 7640 ax-addcl 7641 ax-addrcl 7642 ax-mulcl 7643 ax-addcom 7645 ax-addass 7647 ax-distr 7649 ax-i2m1 7650 ax-0lt1 7651 ax-0id 7653 ax-rnegex 7654 ax-cnre 7656 ax-pre-ltirr 7657 ax-pre-ltwlin 7658 ax-pre-lttrn 7659 ax-pre-ltadd 7661 |
This theorem depends on definitions: df-bi 116 df-dc 803 df-3or 946 df-3an 947 df-tru 1317 df-fal 1320 df-nf 1420 df-sb 1719 df-eu 1978 df-mo 1979 df-clab 2102 df-cleq 2108 df-clel 2111 df-nfc 2244 df-ne 2283 df-nel 2378 df-ral 2395 df-rex 2396 df-reu 2397 df-rab 2399 df-v 2659 df-sbc 2879 df-csb 2972 df-dif 3039 df-un 3041 df-in 3043 df-ss 3050 df-nul 3330 df-if 3441 df-pw 3478 df-sn 3499 df-pr 3500 df-op 3502 df-uni 3703 df-int 3738 df-iun 3781 df-br 3896 df-opab 3950 df-mpt 3951 df-tr 3987 df-id 4175 df-iord 4248 df-on 4250 df-ilim 4251 df-suc 4253 df-iom 4465 df-xp 4505 df-rel 4506 df-cnv 4507 df-co 4508 df-dm 4509 df-rn 4510 df-res 4511 df-ima 4512 df-iota 5046 df-fun 5083 df-fn 5084 df-f 5085 df-f1 5086 df-fo 5087 df-f1o 5088 df-fv 5089 df-riota 5684 df-ov 5731 df-oprab 5732 df-mpo 5733 df-recs 6156 df-frec 6242 df-1o 6267 df-2o 6268 df-map 6498 df-nninf 6957 df-pnf 7726 df-mnf 7727 df-xr 7728 df-ltxr 7729 df-le 7730 df-sub 7858 df-neg 7859 df-inn 8631 df-n0 8882 df-xnn0 8945 df-z 8959 df-uz 9229 |
This theorem is referenced by: (None) |
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