Description: A syllogism inference from two biconditionals. (Contributed by NM, 12-Mar-1993)
Ref | Expression | ||
---|---|---|---|
Hypotheses | bitr4di.1 | |- ( ph -> ( ps <-> ch ) ) |
|
bitr4di.2 | |- ( th <-> ch ) |
||
Assertion | bitr4di | |- ( ph -> ( ps <-> th ) ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | bitr4di.1 | |- ( ph -> ( ps <-> ch ) ) |
|
2 | bitr4di.2 | |- ( th <-> ch ) |
|
3 | 2 | bicomi | |- ( ch <-> th ) |
4 | 1 3 | bitrdi | |- ( ph -> ( ps <-> th ) ) |