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Mirrors > Home > ILE Home > Th. List > inflbti | Unicode version |
Description: An infimum is a lower bound. See also infclti 6825 and infglbti 6827. (Contributed by Jim Kingdon, 18-Dec-2021.) |
Ref | Expression |
---|---|
infclti.ti |
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infclti.ex |
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Ref | Expression |
---|---|
inflbti |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | infclti.ti |
. . . . . 6
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2 | 1 | cnvti 6821 |
. . . . 5
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3 | infclti.ex |
. . . . . 6
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4 | 3 | cnvinfex 6820 |
. . . . 5
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5 | 2, 4 | supubti 6801 |
. . . 4
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6 | 5 | imp 123 |
. . 3
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7 | df-inf 6787 |
. . . . . 6
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8 | 7 | a1i 9 |
. . . . 5
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9 | 8 | breq2d 3887 |
. . . 4
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10 | 2, 4 | supclti 6800 |
. . . . 5
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11 | brcnvg 4658 |
. . . . . 6
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12 | 11 | bicomd 140 |
. . . . 5
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13 | 10, 12 | sylan 279 |
. . . 4
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14 | 9, 13 | bitrd 187 |
. . 3
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15 | 6, 14 | mtbird 639 |
. 2
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16 | 15 | ex 114 |
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 584 ax-in2 585 ax-io 671 ax-5 1391 ax-7 1392 ax-gen 1393 ax-ie1 1437 ax-ie2 1438 ax-8 1450 ax-10 1451 ax-11 1452 ax-i12 1453 ax-bndl 1454 ax-4 1455 ax-14 1460 ax-17 1474 ax-i9 1478 ax-ial 1482 ax-i5r 1483 ax-ext 2082 ax-sep 3986 ax-pow 4038 ax-pr 4069 |
This theorem depends on definitions: df-bi 116 df-3an 932 df-tru 1302 df-fal 1305 df-nf 1405 df-sb 1704 df-eu 1963 df-mo 1964 df-clab 2087 df-cleq 2093 df-clel 2096 df-nfc 2229 df-ral 2380 df-rex 2381 df-reu 2382 df-rmo 2383 df-rab 2384 df-v 2643 df-sbc 2863 df-un 3025 df-in 3027 df-ss 3034 df-pw 3459 df-sn 3480 df-pr 3481 df-op 3483 df-uni 3684 df-br 3876 df-opab 3930 df-cnv 4485 df-iota 5024 df-riota 5662 df-sup 6786 df-inf 6787 |
This theorem is referenced by: zssinfcl 11436 infssuzledc 11438 |
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