Theorem sylani

Description: A syllogism inference. (Contributed by NM, 2-May-1996)

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

Proof

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