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Mirrors > Home > MPE Home > Th. List > clim2c | Structured version Unicode version |
Description: Express the predicate
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Ref | Expression |
---|---|
clim2.1 |
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clim2.2 |
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clim2.3 |
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clim2.4 |
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clim2c.5 |
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clim2c.6 |
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Ref | Expression |
---|---|
clim2c |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | clim2c.5 |
. . 3
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2 | 1 | biantrurd 508 |
. 2
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3 | clim2.1 |
. . . . . . . 8
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4 | 3 | uztrn2 10982 |
. . . . . . 7
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5 | clim2c.6 |
. . . . . . . 8
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6 | 5 | biantrurd 508 |
. . . . . . 7
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7 | 4, 6 | sylan2 474 |
. . . . . 6
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8 | 7 | anassrs 648 |
. . . . 5
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9 | 8 | ralbidva 2839 |
. . . 4
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10 | 9 | rexbidva 2852 |
. . 3
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11 | 10 | ralbidv 2841 |
. 2
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12 | clim2.2 |
. . 3
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13 | clim2.3 |
. . 3
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14 | clim2.4 |
. . 3
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15 | 3, 12, 13, 14 | clim2 13093 |
. 2
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16 | 2, 11, 15 | 3bitr4rd 286 |
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-sep 4514 ax-nul 4522 ax-pow 4571 ax-pr 4632 ax-un 6475 ax-cnex 9442 ax-resscn 9443 ax-pre-lttri 9460 ax-pre-lttrn 9461 |
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-rab 2804 df-v 3073 df-sbc 3288 df-csb 3390 df-dif 3432 df-un 3434 df-in 3436 df-ss 3443 df-nul 3739 df-if 3893 df-pw 3963 df-sn 3979 df-pr 3981 df-op 3985 df-uni 4193 df-br 4394 df-opab 4452 df-mpt 4453 df-id 4737 df-po 4742 df-so 4743 df-xp 4947 df-rel 4948 df-cnv 4949 df-co 4950 df-dm 4951 df-rn 4952 df-res 4953 df-ima 4954 df-iota 5482 df-fun 5521 df-fn 5522 df-f 5523 df-f1 5524 df-fo 5525 df-f1o 5526 df-fv 5527 df-ov 6196 df-er 7204 df-en 7414 df-dom 7415 df-sdom 7416 df-pnf 9524 df-mnf 9525 df-xr 9526 df-ltxr 9527 df-le 9528 df-neg 9702 df-z 10751 df-uz 10966 df-clim 13077 |
This theorem is referenced by: clim0c 13096 climconst 13132 rlimclim1 13134 2clim 13161 climcn1 13180 climcn2 13181 climsqz 13229 climsqz2 13230 climsup 13258 ulmclm 21978 itgulm 21999 climinf 29920 |
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