Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > ILE Home > Th. List > sylbi | GIF version |
Description: A mixed syllogism inference from a biconditional and an implication. Useful for substituting an antecedent with a definition. (Contributed by NM, 5-Aug-1993.) |
Ref | Expression |
---|---|
sylbi.1 | ⊢ (𝜑 ↔ 𝜓) |
sylbi.2 | ⊢ (𝜓 → 𝜒) |
Ref | Expression |
---|---|
sylbi | ⊢ (𝜑 → 𝜒) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | sylbi.1 | . . 3 ⊢ (𝜑 ↔ 𝜓) | |
2 | 1 | biimpi 113 | . 2 ⊢ (𝜑 → 𝜓) |
3 | sylbi.2 | . 2 ⊢ (𝜓 → 𝜒) | |
4 | 2, 3 | syl 14 | 1 ⊢ (𝜑 → 𝜒) |
Copyright terms: Public domain | W3C validator |