Theorem ee100 38908

Description: e100 38907 without virtual deductions. (Contributed by Alan Sare, 23-Jul-2011.) (Proof modification is discouraged.) (New usage is discouraged.)

Hypotheses

Ref	Expression
ee100.1	|- ( ph -> ps )
ee100.2	|- ch
ee100.3	|- th
ee100.4	|- ( ps -> ( ch -> ( th -> ta ) ) )

Assertion

Ref	Expression
ee100	|- ( ph -> ta )

Proof of Theorem ee100

Step	Hyp	Ref	Expression
1		ee100.1	. 2 |- ( ph -> ps )
2		ee100.2	. . 3 |- ch
3	2	a1i 11	. 2 |- ( ph -> ch )
4		ee100.3	. . 3 |- th
5	4	a1i 11	. 2 |- ( ph -> th )
6		ee100.4	. 2 |- ( ps -> ( ch -> ( th -> ta ) ) )
7	1, 3, 5, 6	syl3c 66	1 |- ( ph -> ta )

Syntax hints:   -> wi 4

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7

This theorem is referenced by: (None)