Theorem eel00cT

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

	Ref	Expression
Hypotheses	eel00cT.1	$$⊢\phi$$
	eel00cT.2	$$⊢\psi$$
	eel00cT.3	$$⊢\left(\phi \wedge \psi \right)\to \chi$$
Assertion	eel00cT	$$⊢\top \to \chi$$

Proof

Step	Hyp	Ref	Expression
1		eel00cT.1	$$⊢\phi$$
2		eel00cT.2	$$⊢\psi$$
3		eel00cT.3	$$⊢\left(\phi \wedge \psi \right)\to \chi$$
4	1 3	mpan	$$⊢\psi \to \chi$$
5	2 4	ax-mp	$$⊢\chi$$
6	5	a1i	$$⊢\top \to \chi$$