Theorem eelT00

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

	Ref	Expression
Hypotheses	eelT00.1	|- ( T. -> ph )
	eelT00.2	|- ps
	eelT00.3	|- ch
	eelT00.4	|- ( ( ph /\ ps /\ ch ) -> th )
Assertion	eelT00	|- th

Proof

Step	Hyp	Ref	Expression
1		eelT00.1	|- ( T. -> ph )
2		eelT00.2	|- ps
3		eelT00.3	|- ch
4		eelT00.4	|- ( ( ph /\ ps /\ ch ) -> th )
5		3anass	|- ( ( T. /\ ps /\ ch ) <-> ( T. /\ ( ps /\ ch ) ) )
6		truan	|- ( ( T. /\ ( ps /\ ch ) ) <-> ( ps /\ ch ) )
7	5 6	bitri	|- ( ( T. /\ ps /\ ch ) <-> ( ps /\ ch ) )
8	1 4	syl3an1	|- ( ( T. /\ ps /\ ch ) -> th )
9	7 8	sylbir	|- ( ( ps /\ ch ) -> th )
10	2 9	mpan	|- ( ch -> th )
11	3 10	ax-mp	|- th