Theorem ee200 38873

Description: e200 38872 without virtual deductions. (Contributed by Alan Sare, 13-Jul-2011.) (Proof modification is discouraged.) (New usage is discouraged.)

Hypotheses

Ref	Expression
ee200.1	|- ( ph -> ( ps -> ch ) )
ee200.2	|- th
ee200.3	|- ta
ee200.4	|- ( ch -> ( th -> ( ta -> et ) ) )

Assertion

Ref	Expression
ee200	|- ( ph -> ( ps -> et ) )

Proof of Theorem ee200

Step	Hyp	Ref	Expression
1		ee200.1	. 2 |- ( ph -> ( ps -> ch ) )
2		ee200.2	. . . 4 |- th
3	2	a1i 11	. . 3 |- ( ps -> th )
4	3	a1i 11	. 2 |- ( ph -> ( ps -> th ) )
5		ee200.3	. . . 4 |- ta
6	5	a1i 11	. . 3 |- ( ps -> ta )
7	6	a1i 11	. 2 |- ( ph -> ( ps -> ta ) )
8		ee200.4	. 2 |- ( ch -> ( th -> ( ta -> et ) ) )
9	1, 4, 7, 8	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)