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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 4019 |
. . 3
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2 | xporderlem.1 |
. . . 4
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3 | 2 | eleq2i 2256 |
. . 3
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4 | 1, 3 | bitri 184 |
. 2
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5 | vex 2755 |
. . . 4
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6 | vex 2755 |
. . . 4
![]() ![]() ![]() ![]() | |
7 | 5, 6 | opex 4247 |
. . 3
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8 | vex 2755 |
. . . 4
![]() ![]() ![]() ![]() | |
9 | vex 2755 |
. . . 4
![]() ![]() ![]() ![]() | |
10 | 8, 9 | opex 4247 |
. . 3
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
11 | eleq1 2252 |
. . . . . 6
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12 | opelxp 4674 |
. . . . . 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 6174 |
. . . . . 6
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16 | 15 | breq1d 4028 |
. . . . 5
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
17 | 15 | eqeq1d 2198 |
. . . . . 6
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18 | 5, 6 | op2ndd 6175 |
. . . . . . 7
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19 | 18 | breq1d 4028 |
. . . . . 6
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20 | 17, 19 | anbi12d 473 |
. . . . 5
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21 | 16, 20 | orbi12d 794 |
. . . 4
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22 | 14, 21 | anbi12d 473 |
. . 3
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23 | eleq1 2252 |
. . . . . 6
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24 | opelxp 4674 |
. . . . . 6
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
25 | 23, 24 | bitrdi 196 |
. . . . 5
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26 | 25 | anbi2d 464 |
. . . 4
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27 | 8, 9 | op1std 6174 |
. . . . . 6
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28 | 27 | breq2d 4030 |
. . . . 5
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29 | 27 | eqeq2d 2201 |
. . . . . 6
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30 | 8, 9 | op2ndd 6175 |
. . . . . . 7
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
31 | 30 | breq2d 4030 |
. . . . . 6
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32 | 29, 31 | anbi12d 473 |
. . . . 5
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33 | 28, 32 | orbi12d 794 |
. . . 4
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34 | 26, 33 | anbi12d 473 |
. . 3
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35 | 7, 10, 22, 34 | opelopab 4289 |
. 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 710 ax-5 1458 ax-7 1459 ax-gen 1460 ax-ie1 1504 ax-ie2 1505 ax-8 1515 ax-10 1516 ax-11 1517 ax-i12 1518 ax-bndl 1520 ax-4 1521 ax-17 1537 ax-i9 1541 ax-ial 1545 ax-i5r 1546 ax-13 2162 ax-14 2163 ax-ext 2171 ax-sep 4136 ax-pow 4192 ax-pr 4227 ax-un 4451 |
This theorem depends on definitions: df-bi 117 df-3an 982 df-tru 1367 df-nf 1472 df-sb 1774 df-eu 2041 df-mo 2042 df-clab 2176 df-cleq 2182 df-clel 2185 df-nfc 2321 df-ral 2473 df-rex 2474 df-v 2754 df-sbc 2978 df-un 3148 df-in 3150 df-ss 3157 df-pw 3592 df-sn 3613 df-pr 3614 df-op 3616 df-uni 3825 df-br 4019 df-opab 4080 df-mpt 4081 df-id 4311 df-xp 4650 df-rel 4651 df-cnv 4652 df-co 4653 df-dm 4654 df-rn 4655 df-iota 5196 df-fun 5237 df-fv 5243 df-1st 6166 df-2nd 6167 |
This theorem is referenced by: poxp 6258 |
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