Theorem sylanb

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

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

Proof

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