Theorem eel0001 38945

Description: An elimination deduction. (Contributed by Alan Sare, 17-Oct-2017.)

Hypotheses

Ref	Expression
eel0001.1	|- ph
eel0001.2	|- ps
eel0001.3	|- ch
eel0001.4	|- ( th -> ta )
eel0001.5	|- ( ( ( ( ph /\ ps ) /\ ch ) /\ ta ) -> et )

Assertion

Ref	Expression
eel0001	|- ( th -> et )

Proof of Theorem eel0001

Step	Hyp	Ref	Expression
1		eel0001.3	. 2 |- ch
2		eel0001.4	. 2 |- ( th -> ta )
3		eel0001.1	. . 3 |- ph
4		eel0001.2	. . 3 |- ps
5		eel0001.5	. . . 4 |- ( ( ( ( ph /\ ps ) /\ ch ) /\ ta ) -> et )
6	5	exp41 638	. . 3 |- ( ph -> ( ps -> ( ch -> ( ta -> et ) ) ) )
7	3, 4, 6	mp2 9	. 2 |- ( ch -> ( ta -> et ) )
8	1, 2, 7	mpsyl 68	1 |- ( th -> et )

Syntax hints:   -> wi 4   /\ wa 384

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)