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Mirrors > Home > HOLE Home > Th. List > orval | Unicode version |
Description: Value of the disjunction. (Contributed by Mario Carneiro, 9-Oct-2014.) |
Ref | Expression |
---|---|
imval.1 |
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imval.2 |
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Ref | Expression |
---|---|
orval |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | wor 140 |
. . 3
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2 | imval.1 |
. . 3
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3 | imval.2 |
. . 3
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4 | 1, 2, 3 | wov 72 |
. 2
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5 | df-or 132 |
. . 3
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6 | 1, 2, 3, 5 | oveq 102 |
. 2
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7 | wal 134 |
. . . 4
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8 | wim 137 |
. . . . . 6
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9 | wv 64 |
. . . . . . 7
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10 | wv 64 |
. . . . . . 7
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11 | 8, 9, 10 | wov 72 |
. . . . . 6
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12 | wv 64 |
. . . . . . . 8
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13 | 8, 12, 10 | wov 72 |
. . . . . . 7
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14 | 8, 13, 10 | wov 72 |
. . . . . 6
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15 | 8, 11, 14 | wov 72 |
. . . . 5
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16 | 15 | wl 66 |
. . . 4
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17 | 7, 16 | wc 50 |
. . 3
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18 | 9, 2 | weqi 76 |
. . . . . . . 8
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19 | 18 | id 25 |
. . . . . . 7
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20 | 8, 9, 10, 19 | oveq1 99 |
. . . . . 6
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21 | 8, 11, 14, 20 | oveq1 99 |
. . . . 5
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22 | 15, 21 | leq 91 |
. . . 4
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23 | 7, 16, 22 | ceq2 90 |
. . 3
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24 | 8, 2, 10 | wov 72 |
. . . . . 6
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25 | 8, 24, 14 | wov 72 |
. . . . 5
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26 | 25 | wl 66 |
. . . 4
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27 | 12, 3 | weqi 76 |
. . . . . . . . 9
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28 | 27 | id 25 |
. . . . . . . 8
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29 | 8, 12, 10, 28 | oveq1 99 |
. . . . . . 7
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30 | 8, 13, 10, 29 | oveq1 99 |
. . . . . 6
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31 | 8, 24, 14, 30 | oveq2 101 |
. . . . 5
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32 | 25, 31 | leq 91 |
. . . 4
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33 | 7, 26, 32 | ceq2 90 |
. . 3
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34 | 17, 2, 3, 23, 33 | ovl 117 |
. 2
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35 | 4, 6, 34 | eqtri 95 |
1
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Colors of variables: type var term |
Syntax hints: tv 1
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This theorem was proved from axioms: ax-syl 15 ax-jca 17 ax-simpl 20 ax-simpr 21 ax-id 24 ax-trud 26 ax-cb1 29 ax-cb2 30 ax-wctl 31 ax-wctr 32 ax-weq 40 ax-refl 42 ax-eqmp 45 ax-wc 49 ax-ceq 51 ax-wv 63 ax-wl 65 ax-beta 67 ax-distrc 68 ax-leq 69 ax-distrl 70 ax-wov 71 ax-eqtypi 77 ax-eqtypri 80 ax-hbl1 103 ax-17 105 ax-inst 113 |
This theorem depends on definitions: df-ov 73 df-al 126 df-an 128 df-im 129 df-or 132 |
This theorem is referenced by: ecase 163 olc 164 orc 165 |
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