Description: A mixed syllogism inference from a nested implication and a biconditional. (Contributed by NM, 21-Jun-1993)
Ref | Expression | ||
---|---|---|---|
Hypotheses | imbitrdi.1 | |- ( ph -> ( ps -> ch ) ) |
|
imbitrdi.2 | |- ( ch <-> th ) |
||
Assertion | imbitrdi | |- ( ph -> ( ps -> th ) ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | imbitrdi.1 | |- ( ph -> ( ps -> ch ) ) |
|
2 | imbitrdi.2 | |- ( ch <-> th ) |
|
3 | 2 | biimpi | |- ( ch -> th ) |
4 | 1 3 | syl6 | |- ( ph -> ( ps -> th ) ) |