Description: A mixed syllogism inference from a nested implication and a biconditional. Useful for substituting an embedded antecedent with a definition. (Contributed by NM, 12-Jan-1993)
| Ref | Expression | ||
|---|---|---|---|
| Hypotheses | syl5bi.1 | |- ( ph <-> ps ) |
|
| syl5bi.2 | |- ( ch -> ( ps -> th ) ) |
||
| Assertion | syl5bi | |- ( ch -> ( ph -> th ) ) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | syl5bi.1 | |- ( ph <-> ps ) |
|
| 2 | syl5bi.2 | |- ( ch -> ( ps -> th ) ) |
|
| 3 | 1 | biimpi | |- ( ph -> ps ) |
| 4 | 3 2 | syl5 | |- ( ch -> ( ph -> th ) ) |