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Mirrors > Home > ILE Home > Th. List > mtbi | Unicode version |
Description: An inference from a biconditional, related to modus tollens. (Contributed by NM, 15-Nov-1994.) (Proof shortened by Wolf Lammen, 25-Oct-2012.) |
Ref | Expression |
---|---|
mtbi.1 |
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mtbi.2 |
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Ref | Expression |
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mtbi |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | mtbi.1 |
. 2
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2 | mtbi.2 |
. . 3
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3 | 2 | biimpri 132 |
. 2
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4 | 1, 3 | mto 652 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-in1 604 ax-in2 605 |
This theorem depends on definitions: df-bi 116 |
This theorem is referenced by: mtbir 661 vnex 4067 onsucelsucexmid 4453 dtruex 4482 dmsn0 5014 php5 6760 exmidonfinlem 7066 ndvdsi 11666 nprmi 11841 unennn 11946 bj-vprc 13265 bj-vnex 13267 trirec0xor 13413 |
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