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Mathbox for Jim Kingdon |
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Mirrors > Home > ILE Home > Th. List > Mathboxes > pwf1oexmid | Unicode version |
Description: An exercise related to
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Ref | Expression |
---|---|
pwle2.t |
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Ref | Expression |
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pwf1oexmid |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | pwle2.t |
. . . . . 6
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2 | 1 | pwle2 14404 |
. . . . 5
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3 | 2 | adantr 276 |
. . . 4
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4 | pw1dom2 7220 |
. . . . . 6
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5 | iunxpconst 4683 |
. . . . . . . . . . . 12
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6 | df1o2 6424 |
. . . . . . . . . . . . 13
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7 | 6 | xpeq2i 4644 |
. . . . . . . . . . . 12
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8 | 1, 5, 7 | 3eqtri 2202 |
. . . . . . . . . . 11
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9 | peano1 4590 |
. . . . . . . . . . . 12
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10 | xpsneng 6816 |
. . . . . . . . . . . 12
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11 | 9, 10 | mpan2 425 |
. . . . . . . . . . 11
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12 | 8, 11 | eqbrtrid 4035 |
. . . . . . . . . 10
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13 | 12 | ad2antrr 488 |
. . . . . . . . 9
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14 | 13 | ensymd 6777 |
. . . . . . . 8
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15 | relen 6738 |
. . . . . . . . . 10
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16 | brrelex1 4662 |
. . . . . . . . . 10
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17 | 15, 13, 16 | sylancr 414 |
. . . . . . . . 9
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18 | simplr 528 |
. . . . . . . . . 10
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19 | simpr 110 |
. . . . . . . . . 10
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20 | dff1o5 5466 |
. . . . . . . . . 10
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21 | 18, 19, 20 | sylanbrc 417 |
. . . . . . . . 9
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22 | f1oeng 6751 |
. . . . . . . . 9
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23 | 17, 21, 22 | syl2anc 411 |
. . . . . . . 8
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
24 | entr 6778 |
. . . . . . . 8
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
25 | 14, 23, 24 | syl2anc 411 |
. . . . . . 7
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26 | 25 | ensymd 6777 |
. . . . . 6
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27 | domentr 6785 |
. . . . . 6
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28 | 4, 26, 27 | sylancr 414 |
. . . . 5
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29 | 2onn 6516 |
. . . . . . 7
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30 | nndomo 6858 |
. . . . . . 7
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31 | 29, 30 | mpan 424 |
. . . . . 6
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32 | 31 | ad2antrr 488 |
. . . . 5
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33 | 28, 32 | mpbid 147 |
. . . 4
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34 | 3, 33 | eqssd 3172 |
. . 3
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35 | 26, 34 | breqtrd 4026 |
. . . 4
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36 | exmidpw 6902 |
. . . 4
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37 | 35, 36 | sylibr 134 |
. . 3
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38 | 34, 37 | jca 306 |
. 2
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39 | simplr 528 |
. . . . 5
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40 | 12 | ad2antrr 488 |
. . . . . . . 8
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41 | simprl 529 |
. . . . . . . 8
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42 | 40, 41 | breqtrd 4026 |
. . . . . . 7
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43 | simprr 531 |
. . . . . . . . 9
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44 | 43, 36 | sylib 122 |
. . . . . . . 8
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45 | 44 | ensymd 6777 |
. . . . . . 7
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46 | entr 6778 |
. . . . . . 7
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47 | 42, 45, 46 | syl2anc 411 |
. . . . . 6
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48 | nnfi 6866 |
. . . . . . . 8
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49 | 29, 48 | mp1i 10 |
. . . . . . 7
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50 | enfi 6867 |
. . . . . . . 8
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51 | 44, 50 | syl 14 |
. . . . . . 7
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52 | 49, 51 | mpbird 167 |
. . . . . 6
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53 | f1finf1o 6940 |
. . . . . 6
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54 | 47, 52, 53 | syl2anc 411 |
. . . . 5
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
55 | 39, 54 | mpbid 147 |
. . . 4
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56 | 55, 20 | sylib 122 |
. . 3
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57 | 56 | simprd 114 |
. 2
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58 | 38, 57 | impbida 596 |
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 614 ax-in2 615 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-coll 4115 ax-sep 4118 ax-nul 4126 ax-pow 4171 ax-pr 4206 ax-un 4430 ax-setind 4533 ax-iinf 4584 |
This theorem depends on definitions: df-bi 117 df-dc 835 df-3or 979 df-3an 980 df-tru 1356 df-fal 1359 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-ne 2348 df-ral 2460 df-rex 2461 df-reu 2462 df-rab 2464 df-v 2739 df-sbc 2963 df-csb 3058 df-dif 3131 df-un 3133 df-in 3135 df-ss 3142 df-nul 3423 df-if 3535 df-pw 3576 df-sn 3597 df-pr 3598 df-op 3600 df-uni 3808 df-int 3843 df-iun 3886 df-br 4001 df-opab 4062 df-mpt 4063 df-tr 4099 df-exmid 4192 df-id 4290 df-iord 4363 df-on 4365 df-suc 4368 df-iom 4587 df-xp 4629 df-rel 4630 df-cnv 4631 df-co 4632 df-dm 4633 df-rn 4634 df-res 4635 df-ima 4636 df-iota 5174 df-fun 5214 df-fn 5215 df-f 5216 df-f1 5217 df-fo 5218 df-f1o 5219 df-fv 5220 df-1o 6411 df-2o 6412 df-er 6529 df-en 6735 df-dom 6736 df-fin 6737 |
This theorem is referenced by: (None) |
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