Theorem sylan2br

Description: A syllogism inference. (Contributed by NM, 21-Apr-1994)

	Ref	Expression
Hypotheses	sylan2br.1	$$⊢\chi \leftrightarrow \phi$$
	sylan2br.2	$$⊢\left(\psi \wedge \chi \right)\to \theta$$
Assertion	sylan2br	$$⊢\left(\psi \wedge \phi \right)\to \theta$$

Proof

Step	Hyp	Ref	Expression
1		sylan2br.1	$$⊢\chi \leftrightarrow \phi$$
2		sylan2br.2	$$⊢\left(\psi \wedge \chi \right)\to \theta$$
3	1	biimpri	$$⊢\phi \to \chi$$
4	3 2	sylan2	$$⊢\left(\psi \wedge \phi \right)\to \theta$$