Description: A syllogism inference from two biconditionals. (Contributed by NM, 5-Aug-1993)
Ref | Expression | ||
---|---|---|---|
Hypotheses | bitr2di.1 | |- ( ph -> ( ps <-> ch ) ) |
|
bitr2di.2 | |- ( ch <-> th ) |
||
Assertion | bitr2di | |- ( ph -> ( th <-> ps ) ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | bitr2di.1 | |- ( ph -> ( ps <-> ch ) ) |
|
2 | bitr2di.2 | |- ( ch <-> th ) |
|
3 | 1 2 | bitrdi | |- ( ph -> ( ps <-> th ) ) |
4 | 3 | bicomd | |- ( ph -> ( th <-> ps ) ) |