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Mirrors > Home > ILE Home > Th. List > sbthlemi4 | Unicode version |
Description: Lemma for isbth 6863. (Contributed by NM, 27-Mar-1998.) |
Ref | Expression |
---|---|
sbthlem.1 |
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sbthlem.2 |
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Ref | Expression |
---|---|
sbthlemi4 |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-ima 4560 |
. 2
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2 | dfdm4 4739 |
. . . . . 6
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3 | difss 3207 |
. . . . . . . 8
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
4 | sseq2 3126 |
. . . . . . . 8
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5 | 3, 4 | mpbiri 167 |
. . . . . . 7
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6 | ssdmres 4849 |
. . . . . . 7
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7 | 5, 6 | sylib 121 |
. . . . . 6
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8 | 2, 7 | syl5reqr 2188 |
. . . . 5
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9 | 8 | adantr 274 |
. . . 4
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10 | 9 | 3ad2ant2 1004 |
. . 3
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11 | funcnvres 5204 |
. . . . . . 7
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12 | 11 | 3ad2ant3 1005 |
. . . . . 6
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13 | sbthlem.1 |
. . . . . . . . 9
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14 | sbthlem.2 |
. . . . . . . . 9
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15 | 13, 14 | sbthlemi3 6855 |
. . . . . . . 8
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16 | 15 | reseq2d 4827 |
. . . . . . 7
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17 | 16 | 3adant3 1002 |
. . . . . 6
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18 | 12, 17 | eqtrd 2173 |
. . . . 5
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19 | 18 | rneqd 4776 |
. . . 4
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20 | 19 | 3adant2l 1211 |
. . 3
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21 | 10, 20 | eqtrd 2173 |
. 2
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22 | 1, 21 | eqtr4id 2192 |
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-14 1493 ax-17 1507 ax-i9 1511 ax-ial 1515 ax-i5r 1516 ax-ext 2122 ax-sep 4054 ax-nul 4062 ax-pow 4106 ax-pr 4139 |
This theorem depends on definitions: df-bi 116 df-stab 817 df-dc 821 df-3an 965 df-tru 1335 df-nf 1438 df-sb 1737 df-eu 2003 df-mo 2004 df-clab 2127 df-cleq 2133 df-clel 2136 df-nfc 2271 df-ral 2422 df-rex 2423 df-rab 2426 df-v 2691 df-dif 3078 df-un 3080 df-in 3082 df-ss 3089 df-nul 3369 df-pw 3517 df-sn 3538 df-pr 3539 df-op 3541 df-uni 3745 df-br 3938 df-opab 3998 df-exmid 4127 df-id 4223 df-xp 4553 df-rel 4554 df-cnv 4555 df-co 4556 df-dm 4557 df-rn 4558 df-res 4559 df-ima 4560 df-fun 5133 |
This theorem is referenced by: sbthlemi6 6858 sbthlemi8 6860 |
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