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Mirrors > Home > ILE Home > Th. List > infvalti | Unicode version |
Description: Alternate expression for the infimum. (Contributed by Jim Kingdon, 17-Dec-2021.) |
Ref | Expression |
---|---|
eqinfti.ti |
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infvalti.ex |
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Ref | Expression |
---|---|
infvalti |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-inf 6977 |
. 2
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2 | eqinfti.ti |
. . . . 5
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3 | 2 | cnvti 7011 |
. . . 4
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4 | infvalti.ex |
. . . . 5
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5 | 4 | cnvinfex 7010 |
. . . 4
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6 | 3, 5 | supval2ti 6987 |
. . 3
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7 | vex 2740 |
. . . . . . . . 9
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8 | vex 2740 |
. . . . . . . . 9
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9 | 7, 8 | brcnv 4805 |
. . . . . . . 8
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10 | 9 | a1i 9 |
. . . . . . 7
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11 | 10 | notbid 667 |
. . . . . 6
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12 | 11 | ralbidv 2477 |
. . . . 5
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13 | 8, 7 | brcnv 4805 |
. . . . . . . 8
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14 | 13 | a1i 9 |
. . . . . . 7
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15 | vex 2740 |
. . . . . . . . . 10
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16 | 8, 15 | brcnv 4805 |
. . . . . . . . 9
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17 | 16 | a1i 9 |
. . . . . . . 8
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18 | 17 | rexbidv 2478 |
. . . . . . 7
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19 | 14, 18 | imbi12d 234 |
. . . . . 6
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20 | 19 | ralbidv 2477 |
. . . . 5
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21 | 12, 20 | anbi12d 473 |
. . . 4
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22 | 21 | riotabidv 5826 |
. . 3
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23 | 6, 22 | eqtrd 2210 |
. 2
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24 | 1, 23 | eqtrid 2222 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 106 ax-ia2 107 ax-ia3 108 ax-in1 614 ax-in2 615 ax-io 709 ax-5 1447 ax-7 1448 ax-gen 1449 ax-ie1 1493 ax-ie2 1494 ax-8 1504 ax-10 1505 ax-11 1506 ax-i12 1507 ax-bndl 1509 ax-4 1510 ax-17 1526 ax-i9 1530 ax-ial 1534 ax-i5r 1535 ax-14 2151 ax-ext 2159 ax-sep 4118 ax-pow 4171 ax-pr 4205 |
This theorem depends on definitions: df-bi 117 df-3an 980 df-tru 1356 df-fal 1359 df-nf 1461 df-sb 1763 df-eu 2029 df-mo 2030 df-clab 2164 df-cleq 2170 df-clel 2173 df-nfc 2308 df-ral 2460 df-rex 2461 df-reu 2462 df-rmo 2463 df-rab 2464 df-v 2739 df-sbc 2963 df-un 3133 df-in 3135 df-ss 3142 df-pw 3576 df-sn 3597 df-pr 3598 df-op 3600 df-uni 3808 df-br 4001 df-opab 4062 df-cnv 4630 df-iota 5173 df-riota 5824 df-sup 6976 df-inf 6977 |
This theorem is referenced by: (None) |
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