Theorem ee011 38906

Description: e011 38905 without virtual deductions. (Contributed by Alan Sare, 25-Jul-2011.) (Proof modification is discouraged.) (New usage is discouraged.)

Hypotheses

Ref	Expression
ee011.1	|- ph
ee011.2	|- ( ps -> ch )
ee011.3	|- ( ps -> th )
ee011.4	|- ( ph -> ( ch -> ( th -> ta ) ) )

Assertion

Ref	Expression
ee011	|- ( ps -> ta )

Proof of Theorem ee011

Step	Hyp	Ref	Expression
1		ee011.1	. . 3 |- ph
2	1	a1i 11	. 2 |- ( ps -> ph )
3		ee011.2	. 2 |- ( ps -> ch )
4		ee011.3	. 2 |- ( ps -> th )
5		ee011.4	. 2 |- ( ph -> ( ch -> ( th -> ta ) ) )
6	2, 3, 4, 5	syl3c 66	1 |- ( ps -> 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)