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Mirrors > Home > ILE Home > Th. List > xporderlem | Unicode version |
Description: Lemma for lexicographical ordering theorems. (Contributed by Scott Fenton, 16-Mar-2011.) |
Ref | Expression |
---|---|
xporderlem.1 |
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Ref | Expression |
---|---|
xporderlem |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-br 4001 |
. . 3
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2 | xporderlem.1 |
. . . 4
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3 | 2 | eleq2i 2244 |
. . 3
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4 | 1, 3 | bitri 184 |
. 2
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5 | vex 2740 |
. . . 4
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6 | vex 2740 |
. . . 4
![]() ![]() ![]() ![]() | |
7 | 5, 6 | opex 4226 |
. . 3
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8 | vex 2740 |
. . . 4
![]() ![]() ![]() ![]() | |
9 | vex 2740 |
. . . 4
![]() ![]() ![]() ![]() | |
10 | 8, 9 | opex 4226 |
. . 3
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
11 | eleq1 2240 |
. . . . . 6
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12 | opelxp 4653 |
. . . . . 6
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13 | 11, 12 | bitrdi 196 |
. . . . 5
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14 | 13 | anbi1d 465 |
. . . 4
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15 | 5, 6 | op1std 6143 |
. . . . . 6
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16 | 15 | breq1d 4010 |
. . . . 5
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
17 | 15 | eqeq1d 2186 |
. . . . . 6
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18 | 5, 6 | op2ndd 6144 |
. . . . . . 7
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19 | 18 | breq1d 4010 |
. . . . . 6
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20 | 17, 19 | anbi12d 473 |
. . . . 5
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21 | 16, 20 | orbi12d 793 |
. . . 4
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22 | 14, 21 | anbi12d 473 |
. . 3
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23 | eleq1 2240 |
. . . . . 6
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24 | opelxp 4653 |
. . . . . 6
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25 | 23, 24 | bitrdi 196 |
. . . . 5
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26 | 25 | anbi2d 464 |
. . . 4
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27 | 8, 9 | op1std 6143 |
. . . . . 6
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28 | 27 | breq2d 4012 |
. . . . 5
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29 | 27 | eqeq2d 2189 |
. . . . . 6
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30 | 8, 9 | op2ndd 6144 |
. . . . . . 7
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31 | 30 | breq2d 4012 |
. . . . . 6
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32 | 29, 31 | anbi12d 473 |
. . . . 5
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33 | 28, 32 | orbi12d 793 |
. . . 4
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34 | 26, 33 | anbi12d 473 |
. . 3
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35 | 7, 10, 22, 34 | opelopab 4268 |
. 2
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36 | an4 586 |
. . 3
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37 | 36 | anbi1i 458 |
. 2
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
38 | 4, 35, 37 | 3bitri 206 |
1
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
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-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-13 2150 ax-14 2151 ax-ext 2159 ax-sep 4118 ax-pow 4171 ax-pr 4206 ax-un 4430 |
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-sbc 2963 df-un 3133 df-in 3135 df-ss 3142 df-pw 3576 df-sn 3597 df-pr 3598 df-op 3600 df-uni 3808 df-br 4001 df-opab 4062 df-mpt 4063 df-id 4290 df-xp 4629 df-rel 4630 df-cnv 4631 df-co 4632 df-dm 4633 df-rn 4634 df-iota 5174 df-fun 5214 df-fv 5220 df-1st 6135 df-2nd 6136 |
This theorem is referenced by: poxp 6227 |
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