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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 3938 |
. . 3
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2 | xporderlem.1 |
. . . 4
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3 | 2 | eleq2i 2207 |
. . 3
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4 | 1, 3 | bitri 183 |
. 2
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5 | vex 2692 |
. . . 4
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6 | vex 2692 |
. . . 4
![]() ![]() ![]() ![]() | |
7 | 5, 6 | opex 4159 |
. . 3
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8 | vex 2692 |
. . . 4
![]() ![]() ![]() ![]() | |
9 | vex 2692 |
. . . 4
![]() ![]() ![]() ![]() | |
10 | 8, 9 | opex 4159 |
. . 3
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
11 | eleq1 2203 |
. . . . . 6
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12 | opelxp 4577 |
. . . . . 6
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13 | 11, 12 | syl6bb 195 |
. . . . 5
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14 | 13 | anbi1d 461 |
. . . 4
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15 | 5, 6 | op1std 6054 |
. . . . . 6
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16 | 15 | breq1d 3947 |
. . . . 5
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17 | 15 | eqeq1d 2149 |
. . . . . 6
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18 | 5, 6 | op2ndd 6055 |
. . . . . . 7
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19 | 18 | breq1d 3947 |
. . . . . 6
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20 | 17, 19 | anbi12d 465 |
. . . . 5
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21 | 16, 20 | orbi12d 783 |
. . . 4
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22 | 14, 21 | anbi12d 465 |
. . 3
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23 | eleq1 2203 |
. . . . . 6
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24 | opelxp 4577 |
. . . . . 6
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
25 | 23, 24 | syl6bb 195 |
. . . . 5
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26 | 25 | anbi2d 460 |
. . . 4
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27 | 8, 9 | op1std 6054 |
. . . . . 6
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28 | 27 | breq2d 3949 |
. . . . 5
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29 | 27 | eqeq2d 2152 |
. . . . . 6
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30 | 8, 9 | op2ndd 6055 |
. . . . . . 7
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31 | 30 | breq2d 3949 |
. . . . . 6
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32 | 29, 31 | anbi12d 465 |
. . . . 5
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33 | 28, 32 | orbi12d 783 |
. . . 4
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34 | 26, 33 | anbi12d 465 |
. . 3
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35 | 7, 10, 22, 34 | opelopab 4201 |
. 2
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36 | an4 576 |
. . 3
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37 | 36 | anbi1i 454 |
. 2
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
38 | 4, 35, 37 | 3bitri 205 |
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 105 ax-ia2 106 ax-ia3 107 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-13 1492 ax-14 1493 ax-17 1507 ax-i9 1511 ax-ial 1515 ax-i5r 1516 ax-ext 2122 ax-sep 4054 ax-pow 4106 ax-pr 4139 ax-un 4363 |
This theorem depends on definitions: df-bi 116 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-v 2691 df-sbc 2914 df-un 3080 df-in 3082 df-ss 3089 df-pw 3517 df-sn 3538 df-pr 3539 df-op 3541 df-uni 3745 df-br 3938 df-opab 3998 df-mpt 3999 df-id 4223 df-xp 4553 df-rel 4554 df-cnv 4555 df-co 4556 df-dm 4557 df-rn 4558 df-iota 5096 df-fun 5133 df-fv 5139 df-1st 6046 df-2nd 6047 |
This theorem is referenced by: poxp 6137 |
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