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Mirrors > Home > HOLE Home > Th. List > con2d | Unicode version |
Description: A contraposition deduction. (Contributed by Mario Carneiro, 10-Oct-2014.) |
Ref | Expression |
---|---|
con2d.1 |
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con2d.2 |
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Ref | Expression |
---|---|
con2d |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | con2d.1 |
. . . . 5
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2 | wfal 135 |
. . . . 5
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3 | con2d.2 |
. . . . . 6
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4 | 3 | ax-cb1 29 |
. . . . . . 7
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5 | 1 | notval 145 |
. . . . . . 7
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6 | 4, 5 | a1i 28 |
. . . . . 6
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7 | 3, 6 | mpbi 82 |
. . . . 5
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8 | 1, 2, 7 | imp 157 |
. . . 4
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9 | 8 | an32s 60 |
. . 3
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10 | 9 | ex 158 |
. 2
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11 | 4 | wctl 33 |
. . . 4
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12 | 11, 1 | wct 48 |
. . 3
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13 | 4 | wctr 34 |
. . . 4
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14 | 13 | notval 145 |
. . 3
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15 | 12, 14 | a1i 28 |
. 2
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16 | 10, 15 | mpbir 87 |
1
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Colors of variables: type var term |
Syntax hints: ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
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-fal 127 df-an 128 df-im 129 df-not 130 |
This theorem is referenced by: con3d 162 exnal1 187 |
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