Theorem eelT0 39002

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

Hypotheses

Ref	Expression
eelT0.1	|- ( T. -> ph )
eelT0.2	|- ps
eelT0.3	|- ( ( ph /\ ps ) -> ch )

Assertion

Ref	Expression
eelT0	|- ch

Proof of Theorem eelT0

Step	Hyp	Ref	Expression
1		eelT0.2	. . 3 |- ps
2		eelT0.1	. . . 4 |- ( T. -> ph )
3		eelT0.3	. . . 4 |- ( ( ph /\ ps ) -> ch )
4	2, 3	sylan 488	. . 3 |- ( ( T. /\ ps ) -> ch )
5	1, 4	mpan2 707	. 2 |- ( T. -> ch )
6	5	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)