Theorem ee221 38875

Description: e221 38874 without virtual deductions. (Contributed by Alan Sare, 13-Jul-2011.) (Proof modification is discouraged.) (New usage is discouraged.)

Hypotheses

Ref	Expression
ee221.1	|- ( ph -> ( ps -> ch ) )
ee221.2	|- ( ph -> ( ps -> th ) )
ee221.3	|- ( ph -> ta )
ee221.4	|- ( ch -> ( th -> ( ta -> et ) ) )

Assertion

Ref	Expression
ee221	|- ( ph -> ( ps -> et ) )

Proof of Theorem ee221

Step	Hyp	Ref	Expression
1		ee221.1	. 2 |- ( ph -> ( ps -> ch ) )
2		ee221.2	. 2 |- ( ph -> ( ps -> th ) )
3		ee221.3	. . 3 |- ( ph -> ta )
4	3	a1d 25	. 2 |- ( ph -> ( ps -> ta ) )
5		ee221.4	. 2 |- ( ch -> ( th -> ( ta -> et ) ) )
6	1, 2, 4, 5	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)