Theorem eel00cT 38997

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

Hypotheses

Ref	Expression
eel00cT.1	|- ph
eel00cT.2	|- ps
eel00cT.3	|- ( ( ph /\ ps ) -> ch )

Assertion

Ref	Expression
eel00cT	|- ( T. -> ch )

Proof of Theorem eel00cT

Step	Hyp	Ref	Expression
1		eel00cT.2	. . 3 |- ps
2		eel00cT.1	. . . 4 |- ph
3		eel00cT.3	. . . 4 |- ( ( ph /\ ps ) -> ch )
4	2, 3	mpan 706	. . 3 |- ( ps -> ch )
5	1, 4	ax-mp 5	. 2 |- ch
6	5	a1i 11	1 |- ( T. -> 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

This theorem is referenced by: (None)