Theorem eelT01

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

	Ref	Expression
Hypotheses	eelT01.1	|- ( T. -> ph )
	eelT01.2	|- ps
	eelT01.3	|- ( ch -> th )
	eelT01.4	|- ( ( ph /\ ps /\ th ) -> ta )
Assertion	eelT01	|- ( ch -> ta )

Proof

Step	Hyp	Ref	Expression
1		eelT01.1	|- ( T. -> ph )
2		eelT01.2	|- ps
3		eelT01.3	|- ( ch -> th )
4		eelT01.4	|- ( ( ph /\ ps /\ th ) -> ta )
5		3anass	|- ( ( T. /\ ps /\ ch ) <-> ( T. /\ ( ps /\ ch ) ) )
6		truan	|- ( ( T. /\ ( ps /\ ch ) ) <-> ( ps /\ ch ) )
7		simpr	|- ( ( ps /\ ch ) -> ch )
8	2	jctl	|- ( ch -> ( ps /\ ch ) )
9	7 8	impbii	|- ( ( ps /\ ch ) <-> ch )
10	5 6 9	3bitri	|- ( ( T. /\ ps /\ ch ) <-> ch )
11	1 4	syl3an1	|- ( ( T. /\ ps /\ th ) -> ta )
12	3 11	syl3an3	|- ( ( T. /\ ps /\ ch ) -> ta )
13	10 12	sylbir	|- ( ch -> ta )