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Mirrors > Home > ILE Home > Th. List > eqinftid | Unicode version |
Description: Sufficient condition for an element to be equal to the infimum. (Contributed by Jim Kingdon, 16-Dec-2021.) |
Ref | Expression |
---|---|
eqinfti.ti |
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eqinftid.2 |
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eqinftid.3 |
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eqinftid.4 |
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Ref | Expression |
---|---|
eqinftid |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | eqinftid.2 |
. 2
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2 | eqinftid.3 |
. . 3
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3 | 2 | ralrimiva 2550 |
. 2
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4 | eqinftid.4 |
. . . 4
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5 | 4 | expr 375 |
. . 3
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6 | 5 | ralrimiva 2550 |
. 2
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7 | eqinfti.ti |
. . 3
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8 | 7 | eqinfti 7016 |
. 2
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9 | 1, 3, 6, 8 | mp3and 1340 |
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 4120 ax-pow 4173 ax-pr 4208 |
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 3577 df-sn 3598 df-pr 3599 df-op 3601 df-uni 3810 df-br 4003 df-opab 4064 df-cnv 4633 df-iota 5177 df-riota 5828 df-sup 6980 df-inf 6981 |
This theorem is referenced by: infminti 7023 |
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