Description: A mixed syllogism inference. (Contributed by NM, 19-Jun-2007)
Ref | Expression | ||
---|---|---|---|
Hypotheses | imbitrid.1 | ⊢ ( 𝜑 → 𝜓 ) | |
imbitrid.2 | ⊢ ( 𝜒 → ( 𝜓 ↔ 𝜃 ) ) | ||
Assertion | syl5ibcom | ⊢ ( 𝜑 → ( 𝜒 → 𝜃 ) ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | imbitrid.1 | ⊢ ( 𝜑 → 𝜓 ) | |
2 | imbitrid.2 | ⊢ ( 𝜒 → ( 𝜓 ↔ 𝜃 ) ) | |
3 | 1 2 | imbitrid | ⊢ ( 𝜒 → ( 𝜑 → 𝜃 ) ) |
4 | 3 | com12 | ⊢ ( 𝜑 → ( 𝜒 → 𝜃 ) ) |