Theorem ee102 28943

Description: e102 28942 without virtual deductions. (Contributed by Alan Sare, 14-Jul-2011.) (Proof modification is discouraged.) (New usage is discouraged.)

Hypotheses

Ref	Expression
ee102.1	|- ( ph -> ps )
ee102.2	|- ch
ee102.3	|- ( ph -> ( th -> ta ) )
ee102.4	|- ( ps -> ( ch -> ( ta -> et ) ) )

Assertion

Ref	Expression
ee102	|- ( ph -> ( th -> et ) )

Proof of Theorem ee102

Step	Hyp	Ref	Expression
1		ee102.1	. . 3 |- ( ph -> ps )
2	1	a1d 24	. 2 |- ( ph -> ( th -> ps ) )
3		ee102.2	. . . 4 |- ch
4	3	a1i 11	. . 3 |- ( th -> ch )
5	4	a1i 11	. 2 |- ( ph -> ( th -> ch ) )
6		ee102.3	. 2 |- ( ph -> ( th -> ta ) )
7		ee102.4	. 2 |- ( ps -> ( ch -> ( ta -> et ) ) )
8	2, 5, 6, 7	ee222 28756	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 179  df-an 362