Theorem sylan2i

Description: A syllogism inference. (Contributed by NM, 1-Aug-1994)

	Ref	Expression
Hypotheses	sylan2i.1	⊢ ( 𝜑 → 𝜃 )
	sylan2i.2	⊢ ( 𝜓 → ( ( 𝜒 ∧ 𝜃 ) → 𝜏 ) )
Assertion	sylan2i	⊢ ( 𝜓 → ( ( 𝜒 ∧ 𝜑 ) → 𝜏 ) )

Proof

Step	Hyp	Ref	Expression
1		sylan2i.1	⊢ ( 𝜑 → 𝜃 )
2		sylan2i.2	⊢ ( 𝜓 → ( ( 𝜒 ∧ 𝜃 ) → 𝜏 ) )
3	1	a1i	⊢ ( 𝜓 → ( 𝜑 → 𝜃 ) )
4	3 2	sylan2d	⊢ ( 𝜓 → ( ( 𝜒 ∧ 𝜑 ) → 𝜏 ) )