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Mirrors > Home > ILE Home > Th. List > nebidc | Unicode version |
Description: Contraposition law for inequality. (Contributed by Jim Kingdon, 19-May-2018.) |
Ref | Expression |
---|---|
nebidc |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | id 19 |
. . . 4
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2 | 1 | necon3bid 2321 |
. . 3
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3 | id 19 |
. . . . . . . 8
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4 | 3 | a1d 22 |
. . . . . . 7
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5 | 4 | a1d 22 |
. . . . . 6
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6 | 5 | necon4biddc 2355 |
. . . . 5
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7 | 6 | com3l 81 |
. . . 4
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8 | 7 | imp 123 |
. . 3
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9 | 2, 8 | impbid2 142 |
. 2
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10 | 9 | ex 114 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-in1 586 ax-in2 587 ax-io 681 |
This theorem depends on definitions: df-bi 116 df-stab 799 df-dc 803 df-ne 2281 |
This theorem is referenced by: rpexp 11671 |
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