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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 | |
3imtr3.2 | |
3imtr3.3 |
Ref | Expression |
---|---|
3imtr3i |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | 3imtr3.2 | . . 3 | |
2 | 3imtr3.1 | . . 3 | |
3 | 1, 2 | sylbir 133 | . 2 |
4 | 3imtr3.3 | . 2 | |
5 | 3, 4 | sylib 120 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wb 103 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 104 ax-ia2 105 ax-ia3 106 |
This theorem depends on definitions: df-bi 115 |
This theorem is referenced by: cbv1 1672 moimv 2007 hblem 2186 tfi 4323 smores 5930 idssen 6280 bezoutlemle 10397 |
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