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Mirrors > Home > ILE Home > Th. List > infisoti | Unicode version |
Description: Image of an infimum under an isomorphism. (Contributed by Jim Kingdon, 19-Dec-2021.) |
Ref | Expression |
---|---|
infisoti.1 | |
infisoti.2 | |
infisoti.3 | |
infisoti.ti |
Ref | Expression |
---|---|
infisoti | inf inf |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | infisoti.1 | . . . 4 | |
2 | isocnv2 5472 | . . . 4 | |
3 | 1, 2 | sylib 120 | . . 3 |
4 | infisoti.2 | . . 3 | |
5 | infisoti.3 | . . . 4 | |
6 | 5 | cnvinfex 6431 | . . 3 |
7 | infisoti.ti | . . . 4 | |
8 | 7 | cnvti 6432 | . . 3 |
9 | 3, 4, 6, 8 | supisoti 6423 | . 2 |
10 | df-inf 6398 | . 2 inf | |
11 | df-inf 6398 | . . 3 inf | |
12 | 11 | fveq2i 5201 | . 2 inf |
13 | 9, 10, 12 | 3eqtr4g 2138 | 1 inf inf |
Colors of variables: wff set class |
Syntax hints: wn 3 wi 4 wa 102 wb 103 wceq 1284 wcel 1433 wral 2348 wrex 2349 wss 2973 class class class wbr 3785 ccnv 4362 cima 4366 cfv 4922 wiso 4923 csup 6395 infcinf 6396 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 104 ax-ia2 105 ax-ia3 106 ax-in1 576 ax-in2 577 ax-io 662 ax-5 1376 ax-7 1377 ax-gen 1378 ax-ie1 1422 ax-ie2 1423 ax-8 1435 ax-10 1436 ax-11 1437 ax-i12 1438 ax-bndl 1439 ax-4 1440 ax-14 1445 ax-17 1459 ax-i9 1463 ax-ial 1467 ax-i5r 1468 ax-ext 2063 ax-sep 3896 ax-pow 3948 ax-pr 3964 |
This theorem depends on definitions: df-bi 115 df-3an 921 df-tru 1287 df-fal 1290 df-nf 1390 df-sb 1686 df-eu 1944 df-mo 1945 df-clab 2068 df-cleq 2074 df-clel 2077 df-nfc 2208 df-ral 2353 df-rex 2354 df-reu 2355 df-rmo 2356 df-rab 2357 df-v 2603 df-sbc 2816 df-un 2977 df-in 2979 df-ss 2986 df-pw 3384 df-sn 3404 df-pr 3405 df-op 3407 df-uni 3602 df-br 3786 df-opab 3840 df-mpt 3841 df-id 4048 df-xp 4369 df-rel 4370 df-cnv 4371 df-co 4372 df-dm 4373 df-rn 4374 df-res 4375 df-ima 4376 df-iota 4887 df-fun 4924 df-fn 4925 df-f 4926 df-f1 4927 df-fo 4928 df-f1o 4929 df-fv 4930 df-isom 4931 df-riota 5488 df-sup 6397 df-inf 6398 |
This theorem is referenced by: (None) |
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