Theorem sylan2b

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

	Ref	Expression
Hypotheses	sylan2b.1	$$⊢\phi \leftrightarrow \chi$$
	sylan2b.2	$$⊢\left(\psi \wedge \chi \right)\to \theta$$
Assertion	sylan2b	$$⊢\left(\psi \wedge \phi \right)\to \theta$$

Proof

Step	Hyp	Ref	Expression
1		sylan2b.1	$$⊢\phi \leftrightarrow \chi$$
2		sylan2b.2	$$⊢\left(\psi \wedge \chi \right)\to \theta$$
3	1	biimpi	$$⊢\phi \to \chi$$
4	3 2	sylan2	$$⊢\left(\psi \wedge \phi \right)\to \theta$$