Theorem ee101 38904

Description: e101 38903 without virtual deductions. (Contributed by Alan Sare, 23-Jul-2011.) (Proof modification is discouraged.) (New usage is discouraged.)

Hypotheses

Ref	Expression
ee101.1	|- ( ph -> ps )
ee101.2	|- ch
ee101.3	|- ( ph -> th )
ee101.4	|- ( ps -> ( ch -> ( th -> ta ) ) )

Assertion

Ref	Expression
ee101	|- ( ph -> ta )

Proof of Theorem ee101

Step	Hyp	Ref	Expression
1		ee101.1	. 2 |- ( ph -> ps )
2		ee101.2	. . 3 |- ch
3	2	a1i 11	. 2 |- ( ph -> ch )
4		ee101.3	. 2 |- ( ph -> th )
5		ee101.4	. 2 |- ( ps -> ( ch -> ( th -> ta ) ) )
6	1, 3, 4, 5	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)