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Mirrors > Home > HOLE Home > Th. List > imval | Unicode version |
Description: Value of the implication. (Contributed by Mario Carneiro, 9-Oct-2014.) |
Ref | Expression |
---|---|
imval.1 |
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imval.2 |
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Ref | Expression |
---|---|
imval |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | wim 137 |
. . 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-im 129 |
. . 3
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6 | 1, 2, 3, 5 | oveq 102 |
. 2
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7 | wan 136 |
. . . . 5
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8 | wv 64 |
. . . . 5
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9 | wv 64 |
. . . . 5
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10 | 7, 8, 9 | wov 72 |
. . . 4
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11 | 10, 8 | weqi 76 |
. . 3
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12 | weq 41 |
. . . 4
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13 | 8, 2 | weqi 76 |
. . . . . 6
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14 | 13 | id 25 |
. . . . 5
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15 | 7, 8, 9, 14 | oveq1 99 |
. . . 4
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16 | 12, 10, 8, 15, 14 | oveq12 100 |
. . 3
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17 | 7, 2, 9 | wov 72 |
. . . 4
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18 | 9, 3 | weqi 76 |
. . . . . 6
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19 | 18 | id 25 |
. . . . 5
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20 | 7, 2, 9, 19 | oveq2 101 |
. . . 4
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21 | 12, 17, 2, 20 | oveq1 99 |
. . 3
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22 | 11, 2, 3, 16, 21 | ovl 117 |
. 2
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23 | 4, 6, 22 | 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-an 128 df-im 129 |
This theorem is referenced by: mpd 156 ex 158 |
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