Proof of Theorem nnnq0lem1
Step | Hyp | Ref
| Expression |
1 | | enq0er 7425 |
. . . . . 6
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2 | | erdm 6539 |
. . . . . 6
~Q0
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3 | 1, 2 | ax-mp 5 |
. . . . 5
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4 | | simpll 527 |
. . . . . 6
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("       ~Q0
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~Q0      ~Q0
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5 | | simplll 533 |
. . . . . . . 8
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>." ~Q0
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>." ~Q0  |
6 | 5 | eleq1d 2246 |
. . . . . . 7
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>." ~Q0
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7 | 6 | adantl 277 |
. . . . . 6
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8 | 4, 7 | mpbid 147 |
. . . . 5
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9 | | ecelqsdm 6599 |
. . . . 5
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10 | 3, 8, 9 | sylancr 414 |
. . . 4
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11 | | opelxp 4653 |
. . . 4
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12 | 10, 11 | sylib 122 |
. . 3
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13 | | simprll 537 |
. . . . . . . 8
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14 | 13 | eleq1d 2246 |
. . . . . . 7
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15 | 14 | adantl 277 |
. . . . . 6
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16 | 4, 15 | mpbid 147 |
. . . . 5
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17 | | ecelqsdm 6599 |
. . . . 5
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18 | 3, 16, 17 | sylancr 414 |
. . . 4
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19 | | opelxp 4653 |
. . . 4
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20 | 18, 19 | sylib 122 |
. . 3
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21 | 12, 20 | jca 306 |
. 2
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22 | | simplr 528 |
. . . . . 6
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23 | | simpllr 534 |
. . . . . . . 8
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24 | 23 | eleq1d 2246 |
. . . . . . 7
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25 | 24 | adantl 277 |
. . . . . 6
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26 | 22, 25 | mpbid 147 |
. . . . 5
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27 | | ecelqsdm 6599 |
. . . . 5
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28 | 3, 26, 27 | sylancr 414 |
. . . 4
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29 | | opelxp 4653 |
. . . 4
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30 | 28, 29 | sylib 122 |
. . 3
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31 | | simprlr 538 |
. . . . . . . 8
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32 | 31 | eleq1d 2246 |
. . . . . . 7
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33 | 32 | adantl 277 |
. . . . . 6
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34 | 22, 33 | mpbid 147 |
. . . . 5
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35 | | ecelqsdm 6599 |
. . . . 5
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36 | 3, 34, 35 | sylancr 414 |
. . . 4
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37 | | opelxp 4653 |
. . . 4
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38 | 36, 37 | sylib 122 |
. . 3
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39 | 30, 38 | jca 306 |
. 2
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40 | 5, 13 | eqtr3d 2212 |
. . . . . 6
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>." ~Q0
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41 | 40 | adantl 277 |
. . . . 5
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42 | 1 | a1i 9 |
. . . . . 6
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43 | 42, 10 | erth 6573 |
. . . . 5
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44 | 41, 43 | mpbird 167 |
. . . 4
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45 | | enq0breq 7426 |
. . . . 5
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46 | 12, 20, 45 | syl2anc 411 |
. . . 4
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47 | 44, 46 | mpbid 147 |
. . 3
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48 | 23, 31 | eqtr3d 2212 |
. . . . . 6
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49 | 48 | adantl 277 |
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50 | 42, 28 | erth 6573 |
. . . . 5
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51 | 49, 50 | mpbird 167 |
. . . 4
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52 | | enq0breq 7426 |
. . . . 5
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53 | 30, 38, 52 | syl2anc 411 |
. . . 4
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54 | 51, 53 | mpbid 147 |
. . 3
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55 | 47, 54 | jca 306 |
. 2
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