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Mirrors > Home > MPE Home > Th. List > elkgen | Structured version Visualization version Unicode version |
Description: Value of the compact generator. (Contributed by Mario Carneiro, 20-Mar-2015.) |
Ref | Expression |
---|---|
elkgen |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | kgenval 20605 |
. . 3
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2 | 1 | eleq2d 2525 |
. 2
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3 | ineq1 3639 |
. . . . . . 7
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4 | 3 | eleq1d 2524 |
. . . . . 6
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5 | 4 | imbi2d 322 |
. . . . 5
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6 | 5 | ralbidv 2839 |
. . . 4
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7 | 6 | elrab 3208 |
. . 3
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8 | toponmax 19998 |
. . . . 5
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9 | elpw2g 4583 |
. . . . 5
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10 | 8, 9 | syl 17 |
. . . 4
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11 | 10 | anbi1d 716 |
. . 3
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12 | 7, 11 | syl5bb 265 |
. 2
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13 | 2, 12 | bitrd 261 |
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 |
This theorem depends on definitions: df-bi 190 df-or 376 df-an 377 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-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-xp 4862 df-rel 4863 df-cnv 4864 df-co 4865 df-dm 4866 df-iota 5569 df-fun 5607 df-fv 5613 df-ov 6323 df-top 19976 df-topon 19978 df-kgen 20604 |
This theorem is referenced by: kgeni 20607 kgentopon 20608 kgenss 20613 kgenidm 20617 iskgen3 20619 kgen2ss 20625 kgencn 20626 kgencn3 20628 txkgen 20722 |
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