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Mirrors > Home > ILE Home > Th. List > infclti | Unicode version |
Description: An infimum belongs to its base class (closure law). See also inflbti 6904 and infglbti 6905. (Contributed by Jim Kingdon, 17-Dec-2021.) |
Ref | Expression |
---|---|
infclti.ti | |
infclti.ex |
Ref | Expression |
---|---|
infclti | inf |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-inf 6865 | . 2 inf | |
2 | infclti.ti | . . . 4 | |
3 | 2 | cnvti 6899 | . . 3 |
4 | infclti.ex | . . . 4 | |
5 | 4 | cnvinfex 6898 | . . 3 |
6 | 3, 5 | supclti 6878 | . 2 |
7 | 1, 6 | eqeltrid 2224 | 1 inf |
Colors of variables: wff set class |
Syntax hints: wn 3 wi 4 wa 103 wb 104 wcel 1480 wral 2414 wrex 2415 class class class wbr 3924 ccnv 4533 csup 6862 infcinf 6863 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-in1 603 ax-in2 604 ax-io 698 ax-5 1423 ax-7 1424 ax-gen 1425 ax-ie1 1469 ax-ie2 1470 ax-8 1482 ax-10 1483 ax-11 1484 ax-i12 1485 ax-bndl 1486 ax-4 1487 ax-14 1492 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-ext 2119 ax-sep 4041 ax-pow 4093 ax-pr 4126 |
This theorem depends on definitions: df-bi 116 df-3an 964 df-tru 1334 df-fal 1337 df-nf 1437 df-sb 1736 df-eu 2000 df-mo 2001 df-clab 2124 df-cleq 2130 df-clel 2133 df-nfc 2268 df-ral 2419 df-rex 2420 df-reu 2421 df-rmo 2422 df-rab 2423 df-v 2683 df-sbc 2905 df-un 3070 df-in 3072 df-ss 3079 df-pw 3507 df-sn 3528 df-pr 3529 df-op 3531 df-uni 3732 df-br 3925 df-opab 3985 df-cnv 4542 df-iota 5083 df-riota 5723 df-sup 6864 df-inf 6865 |
This theorem is referenced by: infrenegsupex 9382 supminfex 9385 infxrnegsupex 11025 infssuzledc 11632 |
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