Theorem eelT11

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

	Ref	Expression
Hypotheses	eelT11.1	|- ( T. -> ph )
	eelT11.2	|- ( ps -> ch )
	eelT11.3	|- ( ps -> th )
	eelT11.4	|- ( ( ph /\ ch /\ th ) -> ta )
Assertion	eelT11	|- ( ps -> ta )

Proof

Step	Hyp	Ref	Expression
1		eelT11.1	|- ( T. -> ph )
2		eelT11.2	|- ( ps -> ch )
3		eelT11.3	|- ( ps -> th )
4		eelT11.4	|- ( ( ph /\ ch /\ th ) -> ta )
5		3anass	|- ( ( T. /\ ps /\ ps ) <-> ( T. /\ ( ps /\ ps ) ) )
6		truan	|- ( ( T. /\ ( ps /\ ps ) ) <-> ( ps /\ ps ) )
7		anidm	|- ( ( ps /\ ps ) <-> ps )
8	5 6 7	3bitri	|- ( ( T. /\ ps /\ ps ) <-> ps )
9	1 4	syl3an1	|- ( ( T. /\ ch /\ th ) -> ta )
10	2 9	syl3an2	|- ( ( T. /\ ps /\ th ) -> ta )
11	3 10	syl3an3	|- ( ( T. /\ ps /\ ps ) -> ta )
12	8 11	sylbir	|- ( ps -> ta )