Theorem syl2anbr

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

	Ref	Expression
Hypotheses	syl2anbr.1	$$⊢\psi \leftrightarrow \phi$$
	syl2anbr.2	$$⊢\chi \leftrightarrow \tau$$
	syl2anbr.3	$$⊢\left(\psi \wedge \chi \right)\to \theta$$
Assertion	syl2anbr	$$⊢\left(\phi \wedge \tau \right)\to \theta$$

Proof

Step	Hyp	Ref	Expression
1		syl2anbr.1	$$⊢\psi \leftrightarrow \phi$$
2		syl2anbr.2	$$⊢\chi \leftrightarrow \tau$$
3		syl2anbr.3	$$⊢\left(\psi \wedge \chi \right)\to \theta$$
4	1 3	sylanbr	$$⊢\left(\phi \wedge \chi \right)\to \theta$$
5	2 4	sylan2br	$$⊢\left(\phi \wedge \tau \right)\to \theta$$