Theorem syl3an1

Description: A syllogism inference. (Contributed by NM, 22-Aug-1995)

	Ref	Expression
Hypotheses	syl3an1.1	$$⊢\phi \to \psi$$
	syl3an1.2	$$⊢\left(\psi \wedge \chi \wedge \theta \right)\to \tau$$
Assertion	syl3an1	$$⊢\left(\phi \wedge \chi \wedge \theta \right)\to \tau$$

Proof

Step	Hyp	Ref	Expression
1		syl3an1.1	$$⊢\phi \to \psi$$
2		syl3an1.2	$$⊢\left(\psi \wedge \chi \wedge \theta \right)\to \tau$$
3	1	3anim1i	$$⊢\left(\phi \wedge \chi \wedge \theta \right)\to \left(\psi \wedge \chi \wedge \theta \right)$$
4	3 2	syl	$$⊢\left(\phi \wedge \chi \wedge \theta \right)\to \tau$$