Theorem eelTT1

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

	Ref	Expression
Hypotheses	eelTT1.1	|- ( T. -> ph )
	eelTT1.2	|- ( T. -> ps )
	eelTT1.3	|- ( ch -> th )
	eelTT1.4	|- ( ( ph /\ ps /\ th ) -> ta )
Assertion	eelTT1	|- ( ch -> ta )

Proof

Step	Hyp	Ref	Expression
1		eelTT1.1	|- ( T. -> ph )
2		eelTT1.2	|- ( T. -> ps )
3		eelTT1.3	|- ( ch -> th )
4		eelTT1.4	|- ( ( ph /\ ps /\ th ) -> ta )
5		3anass	|- ( ( T. /\ T. /\ ch ) <-> ( T. /\ ( T. /\ ch ) ) )
6		anabs5	|- ( ( T. /\ ( T. /\ ch ) ) <-> ( T. /\ ch ) )
7		truan	|- ( ( T. /\ ch ) <-> ch )
8	5 6 7	3bitri	|- ( ( T. /\ T. /\ ch ) <-> ch )
9	1 4	syl3an1	|- ( ( T. /\ ps /\ th ) -> ta )
10	2 9	syl3an2	|- ( ( T. /\ T. /\ th ) -> ta )
11	3 10	syl3an3	|- ( ( T. /\ T. /\ ch ) -> ta )
12	8 11	sylbir	|- ( ch -> ta )