Description: A syllogism inference. (Contributed by NM, 31-Jul-2007)
Ref | Expression | ||
---|---|---|---|
Hypotheses | syl3anr1.1 | ⊢ ( 𝜑 → 𝜓 ) | |
syl3anr1.2 | ⊢ ( ( 𝜒 ∧ ( 𝜓 ∧ 𝜃 ∧ 𝜏 ) ) → 𝜂 ) | ||
Assertion | syl3anr1 | ⊢ ( ( 𝜒 ∧ ( 𝜑 ∧ 𝜃 ∧ 𝜏 ) ) → 𝜂 ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | syl3anr1.1 | ⊢ ( 𝜑 → 𝜓 ) | |
2 | syl3anr1.2 | ⊢ ( ( 𝜒 ∧ ( 𝜓 ∧ 𝜃 ∧ 𝜏 ) ) → 𝜂 ) | |
3 | 1 | 3anim1i | ⊢ ( ( 𝜑 ∧ 𝜃 ∧ 𝜏 ) → ( 𝜓 ∧ 𝜃 ∧ 𝜏 ) ) |
4 | 3 2 | sylan2 | ⊢ ( ( 𝜒 ∧ ( 𝜑 ∧ 𝜃 ∧ 𝜏 ) ) → 𝜂 ) |