Theorem syl3an3br

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

	Ref	Expression
Hypotheses	syl3an3br.1	$$⊢\theta \leftrightarrow \phi$$
	syl3an3br.2	$$⊢\left(\psi \wedge \chi \wedge \theta \right)\to \tau$$
Assertion	syl3an3br	$$⊢\left(\psi \wedge \chi \wedge \phi \right)\to \tau$$

Proof

Step	Hyp	Ref	Expression
1		syl3an3br.1	$$⊢\theta \leftrightarrow \phi$$
2		syl3an3br.2	$$⊢\left(\psi \wedge \chi \wedge \theta \right)\to \tau$$
3	1	biimpri	$$⊢\phi \to \theta$$
4	3 2	syl3an3	$$⊢\left(\psi \wedge \chi \wedge \phi \right)\to \tau$$