Theorem eel00000 38949

Description: Elimination rule similar eel0000 38946, except with five hpothesis steps. (Contributed by Alan Sare, 17-Oct-2017.)

Hypotheses

Ref	Expression
eel00000.1	|- ph
eel00000.2	|- ps
eel00000.3	|- ch
eel00000.4	|- th
eel00000.5	|- ta
eel00000.6	|- ( ( ( ( ( ph /\ ps ) /\ ch ) /\ th ) /\ ta ) -> et )

Assertion

Ref	Expression
eel00000	|- et

Proof of Theorem eel00000

Step	Hyp	Ref	Expression
1		eel00000.4	. 2 |- th
2		eel00000.5	. 2 |- ta
3		eel00000.2	. . 3 |- ps
4		eel00000.3	. . 3 |- ch
5		eel00000.1	. . . 4 |- ph
6		eel00000.6	. . . . 5 |- ( ( ( ( ( ph /\ ps ) /\ ch ) /\ th ) /\ ta ) -> et )
7	6	exp41 638	. . . 4 |- ( ( ph /\ ps ) -> ( ch -> ( th -> ( ta -> et ) ) ) )
8	5, 7	mpan 706	. . 3 |- ( ps -> ( ch -> ( th -> ( ta -> et ) ) ) )
9	3, 4, 8	mp2 9	. 2 |- ( th -> ( ta -> et ) )
10	1, 2, 9	mp2 9	1 |- 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)