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Mirrors > Home > ILE Home > Th. List > isoti | Unicode version |
Description: An isomorphism preserves tightness. (Contributed by Jim Kingdon, 26-Nov-2021.) |
Ref | Expression |
---|---|
isoti |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | isocnv 5776 | . . . 4 | |
2 | isotilem 6965 | . . . 4 | |
3 | 1, 2 | syl 14 | . . 3 |
4 | isotilem 6965 | . . 3 | |
5 | 3, 4 | impbid 128 | . 2 |
6 | equequ1 1699 | . . . 4 | |
7 | breq1 3982 | . . . . . 6 | |
8 | 7 | notbid 657 | . . . . 5 |
9 | breq2 3983 | . . . . . 6 | |
10 | 9 | notbid 657 | . . . . 5 |
11 | 8, 10 | anbi12d 465 | . . . 4 |
12 | 6, 11 | bibi12d 234 | . . 3 |
13 | equequ2 1700 | . . . 4 | |
14 | breq2 3983 | . . . . . 6 | |
15 | 14 | notbid 657 | . . . . 5 |
16 | breq1 3982 | . . . . . 6 | |
17 | 16 | notbid 657 | . . . . 5 |
18 | 15, 17 | anbi12d 465 | . . . 4 |
19 | 13, 18 | bibi12d 234 | . . 3 |
20 | 12, 19 | cbvral2v 2703 | . 2 |
21 | 5, 20 | bitrdi 195 | 1 |
Colors of variables: wff set class |
Syntax hints: wn 3 wi 4 wa 103 wb 104 wral 2442 class class class wbr 3979 ccnv 4600 wiso 5186 |
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 604 ax-in2 605 ax-io 699 ax-5 1434 ax-7 1435 ax-gen 1436 ax-ie1 1480 ax-ie2 1481 ax-8 1491 ax-10 1492 ax-11 1493 ax-i12 1494 ax-bndl 1496 ax-4 1497 ax-17 1513 ax-i9 1517 ax-ial 1521 ax-i5r 1522 ax-14 2138 ax-ext 2146 ax-sep 4097 ax-pow 4150 ax-pr 4184 |
This theorem depends on definitions: df-bi 116 df-3an 969 df-tru 1345 df-nf 1448 df-sb 1750 df-eu 2016 df-mo 2017 df-clab 2151 df-cleq 2157 df-clel 2160 df-nfc 2295 df-ral 2447 df-rex 2448 df-v 2726 df-sbc 2950 df-un 3118 df-in 3120 df-ss 3127 df-pw 3558 df-sn 3579 df-pr 3580 df-op 3582 df-uni 3787 df-br 3980 df-opab 4041 df-id 4268 df-xp 4607 df-rel 4608 df-cnv 4609 df-co 4610 df-dm 4611 df-rn 4612 df-res 4613 df-ima 4614 df-iota 5150 df-fun 5187 df-fn 5188 df-f 5189 df-f1 5190 df-fo 5191 df-f1o 5192 df-fv 5193 df-isom 5194 |
This theorem is referenced by: supisoti 6969 |
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