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Mirrors > Home > ILE Home > Th. List > sbthlemi4 | Unicode version |
Description: Lemma for isbth 6980. (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 4651 |
. 2
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2 | difss 3273 |
. . . . . . . 8
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3 | sseq2 3191 |
. . . . . . . 8
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4 | 2, 3 | mpbiri 168 |
. . . . . . 7
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5 | ssdmres 4941 |
. . . . . . 7
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6 | 4, 5 | sylib 122 |
. . . . . 6
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7 | dfdm4 4831 |
. . . . . 6
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8 | 6, 7 | eqtr3di 2235 |
. . . . 5
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9 | 8 | adantr 276 |
. . . 4
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10 | 9 | 3ad2ant2 1020 |
. . 3
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11 | funcnvres 5301 |
. . . . . . 7
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12 | 11 | 3ad2ant3 1021 |
. . . . . 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 6972 |
. . . . . . . 8
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16 | 15 | reseq2d 4919 |
. . . . . . 7
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17 | 16 | 3adant3 1018 |
. . . . . 6
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18 | 12, 17 | eqtrd 2220 |
. . . . 5
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19 | 18 | rneqd 4868 |
. . . 4
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20 | 19 | 3adant2l 1233 |
. . 3
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21 | 10, 20 | eqtrd 2220 |
. 2
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22 | 1, 21 | eqtr4id 2239 |
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 1457 ax-7 1458 ax-gen 1459 ax-ie1 1503 ax-ie2 1504 ax-8 1514 ax-10 1515 ax-11 1516 ax-i12 1517 ax-bndl 1519 ax-4 1520 ax-17 1536 ax-i9 1540 ax-ial 1544 ax-i5r 1545 ax-14 2161 ax-ext 2169 ax-sep 4133 ax-nul 4141 ax-pow 4186 ax-pr 4221 |
This theorem depends on definitions: df-bi 117 df-stab 832 df-dc 836 df-3an 981 df-tru 1366 df-nf 1471 df-sb 1773 df-eu 2039 df-mo 2040 df-clab 2174 df-cleq 2180 df-clel 2183 df-nfc 2318 df-ral 2470 df-rex 2471 df-rab 2474 df-v 2751 df-dif 3143 df-un 3145 df-in 3147 df-ss 3154 df-nul 3435 df-pw 3589 df-sn 3610 df-pr 3611 df-op 3613 df-uni 3822 df-br 4016 df-opab 4077 df-exmid 4207 df-id 4305 df-xp 4644 df-rel 4645 df-cnv 4646 df-co 4647 df-dm 4648 df-rn 4649 df-res 4650 df-ima 4651 df-fun 5230 |
This theorem is referenced by: sbthlemi6 6975 sbthlemi8 6977 |
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