Description: A syllogism deduction. (Contributed by SN, 16-Jul-2024)
Ref | Expression | ||
---|---|---|---|
Hypotheses | sylibda.1 | ⊢ ( 𝜑 → ( 𝜓 ↔ 𝜒 ) ) | |
sylibda.2 | ⊢ ( ( 𝜑 ∧ 𝜒 ) → 𝜃 ) | ||
Assertion | sylibda | ⊢ ( ( 𝜑 ∧ 𝜓 ) → 𝜃 ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | sylibda.1 | ⊢ ( 𝜑 → ( 𝜓 ↔ 𝜒 ) ) | |
2 | sylibda.2 | ⊢ ( ( 𝜑 ∧ 𝜒 ) → 𝜃 ) | |
3 | 1 | biimpa | ⊢ ( ( 𝜑 ∧ 𝜓 ) → 𝜒 ) |
4 | 3 2 | syldan | ⊢ ( ( 𝜑 ∧ 𝜓 ) → 𝜃 ) |