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Mirrors > Home > HOLE Home > Th. List > orc | Unicode version |
Description: Or introduction. (Contributed by Mario Carneiro, 9-Oct-2014.) |
Ref | Expression |
---|---|
olc.1 |
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olc.2 |
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Ref | Expression |
---|---|
orc |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | wim 137 |
. . . 4
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2 | olc.1 |
. . . . 5
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3 | wv 64 |
. . . . 5
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4 | 1, 2, 3 | wov 72 |
. . . 4
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5 | olc.2 |
. . . . . 6
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6 | 1, 5, 3 | wov 72 |
. . . . 5
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7 | 1, 6, 3 | wov 72 |
. . . 4
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8 | 1, 4, 7 | wov 72 |
. . 3
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9 | wtru 43 |
. . . 4
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10 | 2, 4 | simpl 22 |
. . . . . . . . 9
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11 | 2, 4 | simpr 23 |
. . . . . . . . 9
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12 | 3, 10, 11 | mpd 156 |
. . . . . . . 8
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13 | 12, 6 | adantr 55 |
. . . . . . 7
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14 | 13 | ex 158 |
. . . . . 6
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15 | 14 | ex 158 |
. . . . 5
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16 | 15 | eqtru 86 |
. . . 4
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17 | 9, 16 | eqcomi 79 |
. . 3
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18 | 8, 17 | leq 91 |
. 2
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19 | wor 140 |
. . . . 5
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20 | 19, 2, 5 | wov 72 |
. . . 4
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21 | 2, 5 | orval 147 |
. . . 4
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22 | 8 | wl 66 |
. . . . 5
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23 | 22 | alval 142 |
. . . 4
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24 | 20, 21, 23 | eqtri 95 |
. . 3
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25 | 2, 24 | a1i 28 |
. 2
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26 | 18, 25 | mpbir 87 |
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-ded 46 ax-wct 47 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: exmid 199 |
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