Theorem ee012 38893

Description: e012 38892 without virtual deductions. (Contributed by Alan Sare, 14-Jul-2011.) (Proof modification is discouraged.) (New usage is discouraged.)

Hypotheses

Ref	Expression
ee012.1	|- ph
ee012.2	|- ( ps -> ch )
ee012.3	|- ( ps -> ( th -> ta ) )
ee012.4	|- ( ph -> ( ch -> ( ta -> et ) ) )

Assertion

Ref	Expression
ee012	|- ( ps -> ( th -> et ) )

Proof of Theorem ee012

Step	Hyp	Ref	Expression
1		ee012.1	. . . 4 |- ph
2	1	a1i 11	. . 3 |- ( th -> ph )
3	2	a1i 11	. 2 |- ( ps -> ( th -> ph ) )
4		ee012.2	. . 3 |- ( ps -> ch )
5	4	a1d 25	. 2 |- ( ps -> ( th -> ch ) )
6		ee012.3	. 2 |- ( ps -> ( th -> ta ) )
7		ee012.4	. 2 |- ( ph -> ( ch -> ( ta -> et ) ) )
8	3, 5, 6, 7	ee222 38708	1 |- ( ps -> ( th -> 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)