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Mirrors > Home > ILE Home > Th. List > sylnbi | Unicode version |
Description: A mixed syllogism inference from a biconditional and an implication. Useful for substituting an antecedent with a definition. (Contributed by Wolf Lammen, 16-Dec-2013.) |
Ref | Expression |
---|---|
sylnbi.1 | |
sylnbi.2 |
Ref | Expression |
---|---|
sylnbi |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | sylnbi.1 | . . 3 | |
2 | 1 | notbii 663 | . 2 |
3 | sylnbi.2 | . 2 | |
4 | 2, 3 | sylbi 120 | 1 |
Colors of variables: wff set class |
Syntax hints: wn 3 wi 4 wb 104 |
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 609 ax-in2 610 |
This theorem depends on definitions: df-bi 116 |
This theorem is referenced by: sylnbir 674 mo2n 2047 reuun2 3410 regexmidlem1 4515 iotanul 5173 riotaund 5841 snnen2og 6835 |
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