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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 594 | . 2 |
3 | sylnbi.2 | . 2 | |
4 | 2, 3 | sylbi 114 | 1 |
Colors of variables: wff set class |
Syntax hints: wn 3 wi 4 wb 98 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 99 ax-ia2 100 ax-ia3 101 ax-in1 544 ax-in2 545 |
This theorem depends on definitions: df-bi 110 |
This theorem is referenced by: sylnbir 604 mo2n 1928 reuun2 3220 regexmidlem1 4258 iotanul 4882 riotaund 5502 snnen2og 6322 |
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