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Description: Contraposition. Theorem *2.16 of [WhiteheadRussell] p. 103. This version of con3 126 demonstrates the use of the weak deduction theorem dedt 923 to derive it from con3i 127. (Contributed by NM, 27-Jun-2002.) (Proof modification is discouraged.) |
Ref | Expression |
---|---|
con3th |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | id 19 |
. . . 4
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2 | 1 | notbid 285 |
. . 3
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3 | 2 | imbi1d 308 |
. 2
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4 | 1 | imbi2d 307 |
. . . 4
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5 | id 19 |
. . . . 5
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6 | 5 | imbi2d 307 |
. . . 4
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7 | id 19 |
. . . 4
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8 | 4, 6, 7 | elimh 922 |
. . 3
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9 | 8 | con3i 127 |
. 2
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10 | 3, 9 | dedt 923 |
1
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Colors of variables: wff setvar class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 |
This theorem depends on definitions: df-bi 177 df-or 359 df-an 360 |
This theorem is referenced by: (None) |
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