Theorem ee112 38880

Description: e112 38879 without virtual deductions. (Contributed by Alan Sare, 13-Jul-2011.) (Proof modification is discouraged.) (New usage is discouraged.)

Hypotheses

Ref	Expression
ee112.1	|- ( ph -> ps )
ee112.2	|- ( ph -> ch )
ee112.3	|- ( ph -> ( th -> ta ) )
ee112.4	|- ( ps -> ( ch -> ( ta -> et ) ) )

Assertion

Ref	Expression
ee112	|- ( ph -> ( th -> et ) )

Proof of Theorem ee112

Step	Hyp	Ref	Expression
1		ee112.1	. . 3 |- ( ph -> ps )
2	1	a1d 25	. 2 |- ( ph -> ( th -> ps ) )
3		ee112.2	. . 3 |- ( ph -> ch )
4	3	a1d 25	. 2 |- ( ph -> ( th -> ch ) )
5		ee112.3	. 2 |- ( ph -> ( th -> ta ) )
6		ee112.4	. 2 |- ( ps -> ( ch -> ( ta -> et ) ) )
7	2, 4, 5, 6	ee222 38708	1 |- ( ph -> ( 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)