Theorem eelT12

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

	Ref	Expression
Hypotheses	eelT12.1	|- ( T. -> ph )
	eelT12.2	|- ( ps -> ch )
	eelT12.3	|- ( th -> ta )
	eelT12.4	|- ( ( ph /\ ch /\ ta ) -> et )
Assertion	eelT12	|- ( ( ps /\ th ) -> et )

Proof

Step	Hyp	Ref	Expression
1		eelT12.1	|- ( T. -> ph )
2		eelT12.2	|- ( ps -> ch )
3		eelT12.3	|- ( th -> ta )
4		eelT12.4	|- ( ( ph /\ ch /\ ta ) -> et )
5		3anass	|- ( ( T. /\ ps /\ th ) <-> ( T. /\ ( ps /\ th ) ) )
6		truan	|- ( ( T. /\ ( ps /\ th ) ) <-> ( ps /\ th ) )
7	5 6	bitri	|- ( ( T. /\ ps /\ th ) <-> ( ps /\ th ) )
8	1 4	syl3an1	|- ( ( T. /\ ch /\ ta ) -> et )
9	2 8	syl3an2	|- ( ( T. /\ ps /\ ta ) -> et )
10	3 9	syl3an3	|- ( ( T. /\ ps /\ th ) -> et )
11	7 10	sylbir	|- ( ( ps /\ th ) -> et )