Description: A mixed syllogism inference. (Contributed by NM, 12-Jan-1993)
Ref | Expression | ||
---|---|---|---|
Hypotheses | imbitrid.1 | ⊢ ( 𝜑 → 𝜓 ) | |
imbitrid.2 | ⊢ ( 𝜒 → ( 𝜓 ↔ 𝜃 ) ) | ||
Assertion | imbitrid | ⊢ ( 𝜒 → ( 𝜑 → 𝜃 ) ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | imbitrid.1 | ⊢ ( 𝜑 → 𝜓 ) | |
2 | imbitrid.2 | ⊢ ( 𝜒 → ( 𝜓 ↔ 𝜃 ) ) | |
3 | 2 | biimpd | ⊢ ( 𝜒 → ( 𝜓 → 𝜃 ) ) |
4 | 1 3 | syl5 | ⊢ ( 𝜒 → ( 𝜑 → 𝜃 ) ) |