Theorem eel000cT

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

	Ref	Expression
Hypotheses	eel000cT.1	|- ph
	eel000cT.2	|- ps
	eel000cT.3	|- ch
	eel000cT.4	|- ( ( ph /\ ps /\ ch ) -> th )
Assertion	eel000cT	|- ( T. -> th )

Proof

Step	Hyp	Ref	Expression
1		eel000cT.1	|- ph
2		eel000cT.2	|- ps
3		eel000cT.3	|- ch
4		eel000cT.4	|- ( ( ph /\ ps /\ ch ) -> th )
5	1 4	mp3an1	|- ( ( ps /\ ch ) -> th )
6	2 5	mpan	|- ( ch -> th )
7	3 6	ax-mp	|- th
8	7	a1i	|- ( T. -> th )