Theorem eelTT

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

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

Proof

Step	Hyp	Ref	Expression
1		eelTT.1	$$⊢\top \to \phi$$
2		eelTT.2	$$⊢\top \to \psi$$
3		eelTT.3	$$⊢\left(\phi \wedge \psi \right)\to \chi$$
4		truan	$$⊢\left(\top \wedge \psi \right)\leftrightarrow \psi$$
5	1 3	sylan	$$⊢\left(\top \wedge \psi \right)\to \chi$$
6	4 5	sylbir	$$⊢\psi \to \chi$$
7	2 6	syl	$$⊢\top \to \chi$$
8	7	mptru	$$⊢\chi$$