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Mirrors > Home > NFE Home > Th. List > sylnibr | Unicode version |
Description: A mixed syllogism inference from an implication and a biconditional. Useful for substituting a consequent with a definition. (Contributed by Wolf Lammen, 16-Dec-2013.) |
Ref | Expression |
---|---|
sylnibr.1 | |
sylnibr.2 |
Ref | Expression |
---|---|
sylnibr |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | sylnibr.1 | . 2 | |
2 | sylnibr.2 | . . 3 | |
3 | 2 | bicomi 193 | . 2 |
4 | 1, 3 | sylnib 295 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wn 3 wi 4 wb 176 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-3 7 ax-mp 8 |
This theorem depends on definitions: df-bi 177 |
This theorem is referenced by: ncfinraise 4481 tfinltfin 4501 sfindbl 4530 tfinnn 4534 vfinncvntsp 4549 nnc3n3p1 6278 nnc3n3p2 6279 nnc3p1n3p2 6280 nchoicelem2 6290 |
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