Theorem eel0TT

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

	Ref	Expression
Hypotheses	eel0TT.1	|- ph
	eel0TT.2	|- ( T. -> ps )
	eel0TT.3	|- ( T. -> ch )
	eel0TT.4	|- ( ( ph /\ ps /\ ch ) -> th )
Assertion	eel0TT	|- th

Proof

Step	Hyp	Ref	Expression
1		eel0TT.1	|- ph
2		eel0TT.2	|- ( T. -> ps )
3		eel0TT.3	|- ( T. -> ch )
4		eel0TT.4	|- ( ( ph /\ ps /\ ch ) -> th )
5		truan	|- ( ( T. /\ ch ) <-> ch )
6	1 4	mp3an1	|- ( ( ps /\ ch ) -> th )
7	2 6	sylan	|- ( ( T. /\ ch ) -> th )
8	5 7	sylbir	|- ( ch -> th )
9	3 8	syl	|- ( T. -> th )
10	9	mptru	|- th