Theorem ee210 38885

Description: e210 38884 without virtual deductions. (Contributed by Alan Sare, 14-Jul-2011.) (Proof modification is discouraged.) (New usage is discouraged.)

Hypotheses

Ref	Expression
ee210.1	|- ( ph -> ( ps -> ch ) )
ee210.2	|- ( ph -> th )
ee210.3	|- ta
ee210.4	|- ( ch -> ( th -> ( ta -> et ) ) )

Assertion

Ref	Expression
ee210	|- ( ph -> ( ps -> et ) )

Proof of Theorem ee210

Step	Hyp	Ref	Expression
1		ee210.1	. 2 |- ( ph -> ( ps -> ch ) )
2		ee210.2	. . 3 |- ( ph -> th )
3	2	a1d 25	. 2 |- ( ph -> ( ps -> th ) )
4		ee210.3	. . . 4 |- ta
5	4	a1i 11	. . 3 |- ( ps -> ta )
6	5	a1i 11	. 2 |- ( ph -> ( ps -> ta ) )
7		ee210.4	. 2 |- ( ch -> ( th -> ( ta -> et ) ) )
8	1, 3, 6, 7	ee222 38708	1 |- ( ph -> ( ps -> et ) )

Syntax hints:   -> wi 4

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)