Theorem sylanr1

Description: A syllogism inference. (Contributed by NM, 9-Apr-2005)

	Ref	Expression
Hypotheses	sylanr1.1	$$⊢\phi \to \chi$$
	sylanr1.2	$$⊢\left(\psi \wedge \left(\chi \wedge \theta \right)\right)\to \tau$$
Assertion	sylanr1	$$⊢\left(\psi \wedge \left(\phi \wedge \theta \right)\right)\to \tau$$

Proof

Step	Hyp	Ref	Expression
1		sylanr1.1	$$⊢\phi \to \chi$$
2		sylanr1.2	$$⊢\left(\psi \wedge \left(\chi \wedge \theta \right)\right)\to \tau$$
3	1	anim1i	$$⊢\left(\phi \wedge \theta \right)\to \left(\chi \wedge \theta \right)$$
4	3 2	sylan2	$$⊢\left(\psi \wedge \left(\phi \wedge \theta \right)\right)\to \tau$$