Theorem sylan2

Description: A syllogism inference. (Contributed by NM, 21-Apr-1994) (Proof shortened by Wolf Lammen, 22-Nov-2012)

	Ref	Expression
Hypotheses	sylan2.1	$$⊢\phi \to \chi$$
	sylan2.2	$$⊢\left(\psi \wedge \chi \right)\to \theta$$
Assertion	sylan2	$$⊢\left(\psi \wedge \phi \right)\to \theta$$

Proof

Step	Hyp	Ref	Expression
1		sylan2.1	$$⊢\phi \to \chi$$
2		sylan2.2	$$⊢\left(\psi \wedge \chi \right)\to \theta$$
3	1	adantl	$$⊢\left(\psi \wedge \phi \right)\to \chi$$
4	3 2	syldan	$$⊢\left(\psi \wedge \phi \right)\to \theta$$