Description: A syllogism inference from two biconditionals. (Contributed by NM, 5-Aug-1993)
Ref | Expression | ||
---|---|---|---|
Hypotheses | syl6rbb.1 | ⊢ ( 𝜑 → ( 𝜓 ↔ 𝜒 ) ) | |
syl6rbb.2 | ⊢ ( 𝜒 ↔ 𝜃 ) | ||
Assertion | syl6rbb | ⊢ ( 𝜑 → ( 𝜃 ↔ 𝜓 ) ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | syl6rbb.1 | ⊢ ( 𝜑 → ( 𝜓 ↔ 𝜒 ) ) | |
2 | syl6rbb.2 | ⊢ ( 𝜒 ↔ 𝜃 ) | |
3 | 1 2 | syl6bb | ⊢ ( 𝜑 → ( 𝜓 ↔ 𝜃 ) ) |
4 | 3 | bicomd | ⊢ ( 𝜑 → ( 𝜃 ↔ 𝜓 ) ) |