Theorem eelT1

Description: Syllogism inference combined with modus ponens. (Contributed by Jeff Madsen, 2-Sep-2009) (Revised by Alan Sare, 23-Dec-2016) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Hypotheses	eelT1.1	$$⊢\top \to \phi$$
	eelT1.2	$$⊢\psi \to \chi$$
	eelT1.3	$$⊢\left(\phi \wedge \chi \right)\to \theta$$
Assertion	eelT1	$$⊢\psi \to \theta$$

Proof

Step	Hyp	Ref	Expression
1		eelT1.1	$$⊢\top \to \phi$$
2		eelT1.2	$$⊢\psi \to \chi$$
3		eelT1.3	$$⊢\left(\phi \wedge \chi \right)\to \theta$$
4	1	mptru	$$⊢\phi$$
5	4 2 3	sylancr	$$⊢\psi \to \theta$$