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Mirrors > Home > ILE Home > Th. List > 3imtr3i | Unicode version |
Description: A mixed syllogism inference, useful for removing a definition from both sides of an implication. (Contributed by NM, 10-Aug-1994.) |
Ref | Expression |
---|---|
3imtr3.1 |
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3imtr3.2 |
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3imtr3.3 |
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Ref | Expression |
---|---|
3imtr3i |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | 3imtr3.2 |
. . 3
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2 | 3imtr3.1 |
. . 3
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3 | 1, 2 | sylbir 134 |
. 2
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4 | 3imtr3.3 |
. 2
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5 | 3, 4 | sylib 121 |
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 |
This theorem depends on definitions: df-bi 116 |
This theorem is referenced by: cbv1 1723 moimv 2066 hblem 2248 tfi 4504 smores 6197 idssen 6679 suplocsrlem 7640 bezoutlemle 11732 limcmpted 12840 sincosq3sgn 12957 subctctexmid 13369 |
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