Theorem eelTT1 38935

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

Hypotheses

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

Assertion

Ref	Expression
eelTT1	|- ( ch -> ta )

Proof of Theorem eelTT1

Step	Hyp	Ref	Expression
1		3anass 1042	. . 3 |- ( ( T. /\ T. /\ ch ) <-> ( T. /\ ( T. /\ ch ) ) )
2		anabs5 851	. . 3 |- ( ( T. /\ ( T. /\ ch ) ) <-> ( T. /\ ch ) )
3		truan 1501	. . 3 |- ( ( T. /\ ch ) <-> ch )
4	1, 2, 3	3bitri 286	. 2 |- ( ( T. /\ T. /\ ch ) <-> ch )
5		eelTT1.3	. . 3 |- ( ch -> th )
6		eelTT1.2	. . . 4 |- ( T. -> ps )
7		eelTT1.1	. . . . 5 |- ( T. -> ph )
8		eelTT1.4	. . . . 5 |- ( ( ph /\ ps /\ th ) -> ta )
9	7, 8	syl3an1 1359	. . . 4 |- ( ( T. /\ ps /\ th ) -> ta )
10	6, 9	syl3an2 1360	. . 3 |- ( ( T. /\ T. /\ th ) -> ta )
11	5, 10	syl3an3 1361	. 2 |- ( ( T. /\ T. /\ ch ) -> ta )
12	4, 11	sylbir 225	1 |- ( ch -> ta )

Syntax hints:   -> wi 4   /\ wa 384   /\ w3a 1037   T. wtru 1484

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This theorem depends on definitions:  df-bi 197  df-an 386  df-3an 1039  df-tru 1486

This theorem is referenced by: (None)