Theorem sylanbr

Description: A syllogism inference. (Contributed by NM, 18-May-1994)

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

Proof

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