Theorem eel2131

Description: syl2an with antecedents in standard conjunction form. (Contributed by Alan Sare, 26-Aug-2016)

	Ref	Expression
Hypotheses	eel2131.1	$$⊢\left(\phi \wedge \psi \right)\to \chi$$
	eel2131.2	$$⊢\left(\phi \wedge \theta \right)\to \tau$$
	eel2131.3	$$⊢\left(\chi \wedge \tau \right)\to \eta$$
Assertion	eel2131	$$⊢\left(\phi \wedge \psi \wedge \theta \right)\to \eta$$

Proof

Step	Hyp	Ref	Expression
1		eel2131.1	$$⊢\left(\phi \wedge \psi \right)\to \chi$$
2		eel2131.2	$$⊢\left(\phi \wedge \theta \right)\to \tau$$
3		eel2131.3	$$⊢\left(\chi \wedge \tau \right)\to \eta$$
4	1 2 3	syl2an	$$⊢\left(\left(\phi \wedge \psi \right)\wedge \left(\phi \wedge \theta \right)\right)\to \eta$$
5	4	3impdi	$$⊢\left(\phi \wedge \psi \wedge \theta \right)\to \eta$$