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Mirrors > Home > ILE Home > Th. List > sbthlem1 | Unicode version |
Description: Lemma for isbth 6676. (Contributed by NM, 22-Mar-1998.) |
Ref | Expression |
---|---|
sbthlem.1 |
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sbthlem.2 |
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Ref | Expression |
---|---|
sbthlem1 |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | unissb 3683 |
. 2
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2 | sbthlem.2 |
. . . . 5
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3 | 2 | abeq2i 2198 |
. . . 4
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4 | difss2 3128 |
. . . . . . 7
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5 | ssconb 3133 |
. . . . . . . 8
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6 | 5 | exbiri 374 |
. . . . . . 7
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7 | 4, 6 | syl5 32 |
. . . . . 6
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8 | 7 | pm2.43d 49 |
. . . . 5
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9 | 8 | imp 122 |
. . . 4
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10 | 3, 9 | sylbi 119 |
. . 3
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11 | elssuni 3681 |
. . . . 5
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12 | imass2 4808 |
. . . . 5
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13 | sscon 3134 |
. . . . 5
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14 | 11, 12, 13 | 3syl 17 |
. . . 4
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15 | imass2 4808 |
. . . 4
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16 | sscon 3134 |
. . . 4
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17 | 14, 15, 16 | 3syl 17 |
. . 3
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18 | 10, 17 | sstrd 3035 |
. 2
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19 | 1, 18 | mprgbir 2433 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
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 579 ax-in2 580 ax-io 665 ax-5 1381 ax-7 1382 ax-gen 1383 ax-ie1 1427 ax-ie2 1428 ax-8 1440 ax-10 1441 ax-11 1442 ax-i12 1443 ax-bndl 1444 ax-4 1445 ax-17 1464 ax-i9 1468 ax-ial 1472 ax-i5r 1473 ax-ext 2070 |
This theorem depends on definitions: df-bi 115 df-3an 926 df-tru 1292 df-nf 1395 df-sb 1693 df-clab 2075 df-cleq 2081 df-clel 2084 df-nfc 2217 df-ral 2364 df-v 2621 df-dif 3001 df-un 3003 df-in 3005 df-ss 3012 df-sn 3452 df-pr 3453 df-op 3455 df-uni 3654 df-br 3846 df-opab 3900 df-xp 4444 df-cnv 4446 df-dm 4448 df-rn 4449 df-res 4450 df-ima 4451 |
This theorem is referenced by: sbthlem2 6667 sbthlemi3 6668 sbthlemi5 6670 |
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