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Mirrors > Home > ILE Home > Th. List > sbthlem7 | Unicode version |
Description: Lemma for isbth 6959. (Contributed by NM, 27-Mar-1998.) |
Ref | Expression |
---|---|
sbthlem.1 |
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sbthlem.2 |
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sbthlem.3 |
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Ref | Expression |
---|---|
sbthlem7 |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | funres 5252 |
. . 3
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2 | funres 5252 |
. . 3
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3 | dmres 4923 |
. . . . . . . . 9
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4 | inss1 3355 |
. . . . . . . . 9
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5 | 3, 4 | eqsstri 3187 |
. . . . . . . 8
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6 | ssrin 3360 |
. . . . . . . 8
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7 | 5, 6 | ax-mp 5 |
. . . . . . 7
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8 | dmres 4923 |
. . . . . . . . 9
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9 | inss1 3355 |
. . . . . . . . 9
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10 | 8, 9 | eqsstri 3187 |
. . . . . . . 8
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11 | sslin 3361 |
. . . . . . . 8
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12 | 10, 11 | ax-mp 5 |
. . . . . . 7
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13 | 7, 12 | sstri 3164 |
. . . . . 6
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14 | disjdif 3495 |
. . . . . 6
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15 | 13, 14 | sseqtri 3189 |
. . . . 5
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16 | ss0 3463 |
. . . . 5
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17 | 15, 16 | ax-mp 5 |
. . . 4
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18 | funun 5255 |
. . . 4
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19 | 17, 18 | mpan2 425 |
. . 3
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20 | 1, 2, 19 | syl2an 289 |
. 2
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21 | sbthlem.3 |
. . 3
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22 | 21 | funeqi 5232 |
. 2
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23 | 20, 22 | sylibr 134 |
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 614 ax-in2 615 ax-io 709 ax-5 1447 ax-7 1448 ax-gen 1449 ax-ie1 1493 ax-ie2 1494 ax-8 1504 ax-10 1505 ax-11 1506 ax-i12 1507 ax-bndl 1509 ax-4 1510 ax-17 1526 ax-i9 1530 ax-ial 1534 ax-i5r 1535 ax-14 2151 ax-ext 2159 ax-sep 4118 ax-pow 4171 ax-pr 4205 |
This theorem depends on definitions: df-bi 117 df-3an 980 df-tru 1356 df-nf 1461 df-sb 1763 df-eu 2029 df-mo 2030 df-clab 2164 df-cleq 2170 df-clel 2173 df-nfc 2308 df-ral 2460 df-rex 2461 df-v 2739 df-dif 3131 df-un 3133 df-in 3135 df-ss 3142 df-nul 3423 df-pw 3576 df-sn 3597 df-pr 3598 df-op 3600 df-br 4001 df-opab 4062 df-id 4289 df-xp 4628 df-rel 4629 df-cnv 4630 df-co 4631 df-dm 4632 df-res 4634 df-fun 5213 |
This theorem is referenced by: sbthlemi9 6957 |
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