Theorem sylan2i

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

	Ref	Expression
Hypotheses	sylan2i.1	$$⊢\phi \to \theta$$
	sylan2i.2	$$⊢\psi \to \left(\left(\chi \wedge \theta \right)\to \tau \right)$$
Assertion	sylan2i	$$⊢\psi \to \left(\left(\chi \wedge \phi \right)\to \tau \right)$$

Proof

Step	Hyp	Ref	Expression
1		sylan2i.1	$$⊢\phi \to \theta$$
2		sylan2i.2	$$⊢\psi \to \left(\left(\chi \wedge \theta \right)\to \tau \right)$$
3	1	a1i	$$⊢\psi \to \left(\phi \to \theta \right)$$
4	3 2	sylan2d	$$⊢\psi \to \left(\left(\chi \wedge \phi \right)\to \tau \right)$$