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Mirrors > Home > MPE Home > Th. List > clim2c | Structured version Visualization 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 515 |
. 2
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3 | clim2.1 |
. . . . . . . 8
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4 | 3 | uztrn2 11210 |
. . . . . . 7
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5 | clim2c.6 |
. . . . . . . 8
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6 | 5 | biantrurd 515 |
. . . . . . 7
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7 | 4, 6 | sylan2 481 |
. . . . . 6
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8 | 7 | anassrs 658 |
. . . . 5
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9 | 8 | ralbidva 2836 |
. . . 4
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10 | 9 | rexbidva 2910 |
. . 3
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11 | 10 | ralbidv 2839 |
. 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 13623 |
. 2
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16 | 2, 11, 15 | 3bitr4rd 294 |
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 1680 ax-4 1693 ax-5 1769 ax-6 1816 ax-7 1862 ax-8 1900 ax-9 1907 ax-10 1926 ax-11 1931 ax-12 1944 ax-13 2102 ax-ext 2442 ax-sep 4541 ax-nul 4550 ax-pow 4598 ax-pr 4656 ax-un 6615 ax-cnex 9626 ax-resscn 9627 ax-pre-lttri 9644 ax-pre-lttrn 9645 |
This theorem depends on definitions: df-bi 190 df-or 376 df-an 377 df-3or 992 df-3an 993 df-tru 1458 df-ex 1675 df-nf 1679 df-sb 1809 df-eu 2314 df-mo 2315 df-clab 2449 df-cleq 2455 df-clel 2458 df-nfc 2592 df-ne 2635 df-nel 2636 df-ral 2754 df-rex 2755 df-rab 2758 df-v 3059 df-sbc 3280 df-csb 3376 df-dif 3419 df-un 3421 df-in 3423 df-ss 3430 df-nul 3744 df-if 3894 df-pw 3965 df-sn 3981 df-pr 3983 df-op 3987 df-uni 4213 df-br 4419 df-opab 4478 df-mpt 4479 df-id 4771 df-po 4777 df-so 4778 df-xp 4862 df-rel 4863 df-cnv 4864 df-co 4865 df-dm 4866 df-rn 4867 df-res 4868 df-ima 4869 df-iota 5569 df-fun 5607 df-fn 5608 df-f 5609 df-f1 5610 df-fo 5611 df-f1o 5612 df-fv 5613 df-ov 6323 df-er 7394 df-en 7601 df-dom 7602 df-sdom 7603 df-pnf 9708 df-mnf 9709 df-xr 9710 df-ltxr 9711 df-le 9712 df-neg 9894 df-z 10972 df-uz 11194 df-clim 13607 |
This theorem is referenced by: clim0c 13626 climconst 13662 rlimclim1 13664 2clim 13691 climcn1 13710 climcn2 13711 climsqz 13759 climsqz2 13760 climsup 13788 ulmclm 23398 itgulm 23419 climinf 37770 climinfOLD 37771 |
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