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	|- ( T. -> ph )
	eelTT.2	|- ( T. -> ps )
	eelTT.3	|- ( ( ph /\ ps ) -> ch )
Assertion	eelTT	|- ch

Proof

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