Description: A mixed syllogism inference. (Contributed by NM, 20-Jun-2007)
Ref | Expression | ||
---|---|---|---|
Hypotheses | imbitrrid.1 | ⊢ ( 𝜑 → 𝜃 ) | |
imbitrrid.2 | ⊢ ( 𝜒 → ( 𝜓 ↔ 𝜃 ) ) | ||
Assertion | syl5ibrcom | ⊢ ( 𝜑 → ( 𝜒 → 𝜓 ) ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | imbitrrid.1 | ⊢ ( 𝜑 → 𝜃 ) | |
2 | imbitrrid.2 | ⊢ ( 𝜒 → ( 𝜓 ↔ 𝜃 ) ) | |
3 | 1 2 | imbitrrid | ⊢ ( 𝜒 → ( 𝜑 → 𝜓 ) ) |
4 | 3 | com12 | ⊢ ( 𝜑 → ( 𝜒 → 𝜓 ) ) |