Description: A mixed syllogism inference. (Contributed by NM, 3-Apr-1994)
Ref | Expression | ||
---|---|---|---|
Hypotheses | imbitrrid.1 | ⊢ ( 𝜑 → 𝜃 ) | |
imbitrrid.2 | ⊢ ( 𝜒 → ( 𝜓 ↔ 𝜃 ) ) | ||
Assertion | imbitrrid | ⊢ ( 𝜒 → ( 𝜑 → 𝜓 ) ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | imbitrrid.1 | ⊢ ( 𝜑 → 𝜃 ) | |
2 | imbitrrid.2 | ⊢ ( 𝜒 → ( 𝜓 ↔ 𝜃 ) ) | |
3 | 2 | bicomd | ⊢ ( 𝜒 → ( 𝜃 ↔ 𝜓 ) ) |
4 | 1 3 | imbitrid | ⊢ ( 𝜒 → ( 𝜑 → 𝜓 ) ) |