Theorem eelT0

Description: An elimination deduction. (Contributed by Alan Sare, 4-Feb-2017) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Hypotheses	eelT0.1	$$⊢\top \to \phi$$
	eelT0.2	$$⊢\psi$$
	eelT0.3	$$⊢\left(\phi \wedge \psi \right)\to \chi$$
Assertion	eelT0	$$⊢\chi$$

Proof

Step	Hyp	Ref	Expression
1		eelT0.1	$$⊢\top \to \phi$$
2		eelT0.2	$$⊢\psi$$
3		eelT0.3	$$⊢\left(\phi \wedge \psi \right)\to \chi$$
4	1 3	sylan	$$⊢\left(\top \wedge \psi \right)\to \chi$$
5	2 4	mpan2	$$⊢\top \to \chi$$
6	5	mptru	$$⊢\chi$$