Theorem ee211 38883

Description: e211 38882 without virtual deductions. (Contributed by Alan Sare, 13-Jul-2011.) (Proof modification is discouraged.) (New usage is discouraged.)

Hypotheses

Ref	Expression
ee211.1	|- ( ph -> ( ps -> ch ) )
ee211.2	|- ( ph -> th )
ee211.3	|- ( ph -> ta )
ee211.4	|- ( ch -> ( th -> ( ta -> et ) ) )

Assertion

Ref	Expression
ee211	|- ( ph -> ( ps -> et ) )

Proof of Theorem ee211

Step	Hyp	Ref	Expression
1		ee211.1	. 2 |- ( ph -> ( ps -> ch ) )
2		ee211.2	. . 3 |- ( ph -> th )
3	2	a1d 25	. 2 |- ( ph -> ( ps -> th ) )
4		ee211.3	. . 3 |- ( ph -> ta )
5	4	a1d 25	. 2 |- ( ph -> ( ps -> ta ) )
6		ee211.4	. 2 |- ( ch -> ( th -> ( ta -> et ) ) )
7	1, 3, 5, 6	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)