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Mirrors > Home > ILE Home > Th. List > sbthlemi4 | Unicode version |
Description: Lemma for isbth 6783. (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 | dfdm4 4669 |
. . . . . 6
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2 | difss 3149 |
. . . . . . . 8
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3 | sseq2 3071 |
. . . . . . . 8
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4 | 2, 3 | mpbiri 167 |
. . . . . . 7
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
5 | ssdmres 4777 |
. . . . . . 7
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6 | 4, 5 | sylib 121 |
. . . . . 6
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7 | 1, 6 | syl5reqr 2147 |
. . . . 5
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8 | 7 | adantr 272 |
. . . 4
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9 | 8 | 3ad2ant2 971 |
. . 3
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10 | funcnvres 5132 |
. . . . . . 7
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11 | 10 | 3ad2ant3 972 |
. . . . . 6
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12 | sbthlem.1 |
. . . . . . . . 9
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13 | sbthlem.2 |
. . . . . . . . 9
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14 | 12, 13 | sbthlemi3 6775 |
. . . . . . . 8
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15 | 14 | reseq2d 4755 |
. . . . . . 7
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16 | 15 | 3adant3 969 |
. . . . . 6
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17 | 11, 16 | eqtrd 2132 |
. . . . 5
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18 | 17 | rneqd 4706 |
. . . 4
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19 | 18 | 3adant2l 1178 |
. . 3
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20 | 9, 19 | eqtrd 2132 |
. 2
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21 | df-ima 4490 |
. 2
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22 | 20, 21 | syl6reqr 2151 |
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 105 ax-ia2 106 ax-ia3 107 ax-in1 584 ax-in2 585 ax-io 671 ax-5 1391 ax-7 1392 ax-gen 1393 ax-ie1 1437 ax-ie2 1438 ax-8 1450 ax-10 1451 ax-11 1452 ax-i12 1453 ax-bndl 1454 ax-4 1455 ax-14 1460 ax-17 1474 ax-i9 1478 ax-ial 1482 ax-i5r 1483 ax-ext 2082 ax-sep 3986 ax-nul 3994 ax-pow 4038 ax-pr 4069 |
This theorem depends on definitions: df-bi 116 df-stab 782 df-dc 787 df-3an 932 df-tru 1302 df-nf 1405 df-sb 1704 df-eu 1963 df-mo 1964 df-clab 2087 df-cleq 2093 df-clel 2096 df-nfc 2229 df-ral 2380 df-rex 2381 df-rab 2384 df-v 2643 df-dif 3023 df-un 3025 df-in 3027 df-ss 3034 df-nul 3311 df-pw 3459 df-sn 3480 df-pr 3481 df-op 3483 df-uni 3684 df-br 3876 df-opab 3930 df-exmid 4059 df-id 4153 df-xp 4483 df-rel 4484 df-cnv 4485 df-co 4486 df-dm 4487 df-rn 4488 df-res 4489 df-ima 4490 df-fun 5061 |
This theorem is referenced by: sbthlemi6 6778 sbthlemi8 6780 |
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