Theorem eel0000 38946

Description: Elimination rule similar to mp4an 709, except with a left-nested conjunction unification theorem. (Contributed by Alan Sare, 17-Oct-2017.)

Hypotheses

Ref	Expression
eel0000.1	|- ph
eel0000.2	|- ps
eel0000.3	|- ch
eel0000.4	|- th
eel0000.5	|- ( ( ( ( ph /\ ps ) /\ ch ) /\ th ) -> ta )

Assertion

Ref	Expression
eel0000	|- ta

Proof of Theorem eel0000

Step	Hyp	Ref	Expression
1		eel0000.3	. 2 |- ch
2		eel0000.4	. 2 |- th
3		eel0000.1	. . 3 |- ph
4		eel0000.2	. . 3 |- ps
5		eel0000.5	. . . 4 |- ( ( ( ( ph /\ ps ) /\ ch ) /\ th ) -> ta )
6	5	exp41 638	. . 3 |- ( ph -> ( ps -> ( ch -> ( th -> ta ) ) ) )
7	3, 4, 6	mp2 9	. 2 |- ( ch -> ( th -> ta ) )
8	1, 2, 7	mp2 9	1 |- ta

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)