Theorem syl3an2

Description: A syllogism inference. (Contributed by NM, 22-Aug-1995) (Proof shortened by Wolf Lammen, 26-Jun-2022)

	Ref	Expression
Hypotheses	syl3an2.1	$$⊢\phi \to \chi$$
	syl3an2.2	$$⊢\left(\psi \wedge \chi \wedge \theta \right)\to \tau$$
Assertion	syl3an2	$$⊢\left(\psi \wedge \phi \wedge \theta \right)\to \tau$$

Proof

Step	Hyp	Ref	Expression
1		syl3an2.1	$$⊢\phi \to \chi$$
2		syl3an2.2	$$⊢\left(\psi \wedge \chi \wedge \theta \right)\to \tau$$
3	1	3anim2i	$$⊢\left(\psi \wedge \phi \wedge \theta \right)\to \left(\psi \wedge \chi \wedge \theta \right)$$
4	3 2	syl	$$⊢\left(\psi \wedge \phi \wedge \theta \right)\to \tau$$