Description: A syllogism inference from two biconditionals. (Contributed by NM, 1-Aug-1993)
Ref | Expression | ||
---|---|---|---|
Hypotheses | bitr2id.1 | |- ( ph <-> ps ) |
|
bitr2id.2 | |- ( ch -> ( ps <-> th ) ) |
||
Assertion | bitr2id | |- ( ch -> ( th <-> ph ) ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | bitr2id.1 | |- ( ph <-> ps ) |
|
2 | bitr2id.2 | |- ( ch -> ( ps <-> th ) ) |
|
3 | 1 2 | bitrid | |- ( ch -> ( ph <-> th ) ) |
4 | 3 | bicomd | |- ( ch -> ( th <-> ph ) ) |