Theorem eelTT 38998

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

Hypotheses

Ref	Expression
eelTT.1	|- ( T. -> ph )
eelTT.2	|- ( T. -> ps )
eelTT.3	|- ( ( ph /\ ps ) -> ch )

Assertion

Ref	Expression
eelTT	|- ch

Proof of Theorem eelTT

Step	Hyp	Ref	Expression
1		eelTT.2	. . 3 |- ( T. -> ps )
2		truan 1501	. . . 4 |- ( ( T. /\ ps ) <-> ps )
3		eelTT.1	. . . . 5 |- ( T. -> ph )
4		eelTT.3	. . . . 5 |- ( ( ph /\ ps ) -> ch )
5	3, 4	sylan 488	. . . 4 |- ( ( T. /\ ps ) -> ch )
6	2, 5	sylbir 225	. . 3 |- ( ps -> ch )
7	1, 6	syl 17	. 2 |- ( T. -> ch )
8	7	trud 1493	1 |- ch

Syntax hints:   -> wi 4   /\ wa 384   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-tru 1486

This theorem is referenced by: (None)