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Mirrors > Home > HOLE Home > Th. List > ecase | Unicode version |
Description: Elimination by cases. (Contributed by Mario Carneiro, 9-Oct-2014.) |
Ref | Expression |
---|---|
ecase.1 |
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ecase.2 |
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ecase.3 |
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ecase.4 |
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ecase.5 |
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ecase.6 |
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Ref | Expression |
---|---|
ecase |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ecase.3 |
. 2
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2 | ecase.6 |
. . 3
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3 | 2 | ex 158 |
. 2
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4 | wim 137 |
. . . 4
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5 | ecase.2 |
. . . . 5
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6 | 4, 5, 1 | wov 72 |
. . . 4
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7 | 4, 6, 1 | wov 72 |
. . 3
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8 | ecase.5 |
. . . 4
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9 | 8 | ex 158 |
. . 3
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10 | ecase.4 |
. . . . 5
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11 | 10 | ax-cb1 29 |
. . . . . 6
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12 | ecase.1 |
. . . . . . 7
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13 | 12, 5 | orval 147 |
. . . . . 6
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
14 | 11, 13 | a1i 28 |
. . . . 5
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15 | 10, 14 | mpbi 82 |
. . . 4
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16 | wv 64 |
. . . . . . 7
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17 | 4, 12, 16 | wov 72 |
. . . . . 6
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18 | 4, 5, 16 | wov 72 |
. . . . . . 7
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19 | 4, 18, 16 | wov 72 |
. . . . . 6
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20 | 4, 17, 19 | wov 72 |
. . . . 5
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21 | 16, 1 | weqi 76 |
. . . . . . . 8
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22 | 21 | id 25 |
. . . . . . 7
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23 | 4, 12, 16, 22 | oveq2 101 |
. . . . . 6
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24 | 4, 5, 16, 22 | oveq2 101 |
. . . . . . 7
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25 | 4, 18, 16, 24, 22 | oveq12 100 |
. . . . . 6
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26 | 4, 17, 19, 23, 25 | oveq12 100 |
. . . . 5
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
27 | 20, 1, 26 | cla4v 152 |
. . . 4
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
28 | 15, 27 | syl 16 |
. . 3
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
29 | 7, 9, 28 | mpd 156 |
. 2
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30 | 1, 3, 29 | mpd 156 |
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 notnot 200 ax3 205 |
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