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Mirrors > Home > ILE Home > Th. List > sbthlem1 | Unicode version |
Description: Lemma for isbth 6863. (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 3774 |
. 2
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2 | sbthlem.2 |
. . . . 5
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3 | 2 | abeq2i 2251 |
. . . 4
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4 | difss2 3209 |
. . . . . . 7
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5 | ssconb 3214 |
. . . . . . . 8
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6 | 5 | exbiri 380 |
. . . . . . 7
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7 | 4, 6 | syl5 32 |
. . . . . 6
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8 | 7 | pm2.43d 50 |
. . . . 5
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9 | 8 | imp 123 |
. . . 4
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10 | 3, 9 | sylbi 120 |
. . 3
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11 | elssuni 3772 |
. . . . 5
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12 | imass2 4923 |
. . . . 5
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13 | sscon 3215 |
. . . . 5
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14 | 11, 12, 13 | 3syl 17 |
. . . 4
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15 | imass2 4923 |
. . . 4
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16 | sscon 3215 |
. . . 4
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17 | 14, 15, 16 | 3syl 17 |
. . 3
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18 | 10, 17 | sstrd 3112 |
. 2
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19 | 1, 18 | mprgbir 2493 |
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 105 ax-ia2 106 ax-ia3 107 ax-in1 604 ax-in2 605 ax-io 699 ax-5 1424 ax-7 1425 ax-gen 1426 ax-ie1 1470 ax-ie2 1471 ax-8 1483 ax-10 1484 ax-11 1485 ax-i12 1486 ax-bndl 1487 ax-4 1488 ax-17 1507 ax-i9 1511 ax-ial 1515 ax-i5r 1516 ax-ext 2122 |
This theorem depends on definitions: df-bi 116 df-3an 965 df-tru 1335 df-nf 1438 df-sb 1737 df-clab 2127 df-cleq 2133 df-clel 2136 df-nfc 2271 df-ral 2422 df-v 2691 df-dif 3078 df-un 3080 df-in 3082 df-ss 3089 df-sn 3538 df-pr 3539 df-op 3541 df-uni 3745 df-br 3938 df-opab 3998 df-xp 4553 df-cnv 4555 df-dm 4557 df-rn 4558 df-res 4559 df-ima 4560 |
This theorem is referenced by: sbthlem2 6854 sbthlemi3 6855 sbthlemi5 6857 |
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