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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 |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | isocnv 5829 |
. . . 4
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2 | isotilem 7030 |
. . . 4
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3 | 1, 2 | syl 14 |
. . 3
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4 | isotilem 7030 |
. . 3
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5 | 3, 4 | impbid 129 |
. 2
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6 | equequ1 1723 |
. . . 4
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7 | breq1 4021 |
. . . . . 6
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8 | 7 | notbid 668 |
. . . . 5
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9 | breq2 4022 |
. . . . . 6
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10 | 9 | notbid 668 |
. . . . 5
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11 | 8, 10 | anbi12d 473 |
. . . 4
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12 | 6, 11 | bibi12d 235 |
. . 3
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13 | equequ2 1724 |
. . . 4
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14 | breq2 4022 |
. . . . . 6
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15 | 14 | notbid 668 |
. . . . 5
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16 | breq1 4021 |
. . . . . 6
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17 | 16 | notbid 668 |
. . . . 5
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18 | 15, 17 | anbi12d 473 |
. . . 4
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19 | 13, 18 | bibi12d 235 |
. . 3
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20 | 12, 19 | cbvral2v 2731 |
. 2
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21 | 5, 20 | bitrdi 196 |
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 615 ax-in2 616 ax-io 710 ax-5 1458 ax-7 1459 ax-gen 1460 ax-ie1 1504 ax-ie2 1505 ax-8 1515 ax-10 1516 ax-11 1517 ax-i12 1518 ax-bndl 1520 ax-4 1521 ax-17 1537 ax-i9 1541 ax-ial 1545 ax-i5r 1546 ax-14 2163 ax-ext 2171 ax-sep 4136 ax-pow 4189 ax-pr 4224 |
This theorem depends on definitions: df-bi 117 df-3an 982 df-tru 1367 df-nf 1472 df-sb 1774 df-eu 2041 df-mo 2042 df-clab 2176 df-cleq 2182 df-clel 2185 df-nfc 2321 df-ral 2473 df-rex 2474 df-v 2754 df-sbc 2978 df-un 3148 df-in 3150 df-ss 3157 df-pw 3592 df-sn 3613 df-pr 3614 df-op 3616 df-uni 3825 df-br 4019 df-opab 4080 df-id 4308 df-xp 4647 df-rel 4648 df-cnv 4649 df-co 4650 df-dm 4651 df-rn 4652 df-res 4653 df-ima 4654 df-iota 5193 df-fun 5234 df-fn 5235 df-f 5236 df-f1 5237 df-fo 5238 df-f1o 5239 df-fv 5240 df-isom 5241 |
This theorem is referenced by: supisoti 7034 |
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