Theorem syl2anb

Description: A double syllogism inference. (Contributed by NM, 29-Jul-1999)

	Ref	Expression
Hypotheses	syl2anb.1	$$⊢\phi \leftrightarrow \psi$$
	syl2anb.2	$$⊢\tau \leftrightarrow \chi$$
	syl2anb.3	$$⊢\left(\psi \wedge \chi \right)\to \theta$$
Assertion	syl2anb	$$⊢\left(\phi \wedge \tau \right)\to \theta$$

Proof

Step	Hyp	Ref	Expression
1		syl2anb.1	$$⊢\phi \leftrightarrow \psi$$
2		syl2anb.2	$$⊢\tau \leftrightarrow \chi$$
3		syl2anb.3	$$⊢\left(\psi \wedge \chi \right)\to \theta$$
4	1 3	sylanb	$$⊢\left(\phi \wedge \chi \right)\to \theta$$
5	2 4	sylan2b	$$⊢\left(\phi \wedge \tau \right)\to \theta$$