Theorem ee13 38710

Description: e13 38975 without virtual deduction connectives. Special theorem needed for the Virtual Deduction translation tool. (Contributed by Alan Sare, 28-Oct-2011.) (Proof modification is discouraged.) (New usage is discouraged.)

Hypotheses

Ref	Expression
ee13.1	|- ( ph -> ps )
ee13.2	|- ( ph -> ( ch -> ( th -> ta ) ) )
ee13.3	|- ( ps -> ( ta -> et ) )

Assertion

Ref	Expression
ee13	|- ( ph -> ( ch -> ( th -> et ) ) )

Proof of Theorem ee13

Step	Hyp	Ref	Expression
1		ee13.2	. 2 |- ( ph -> ( ch -> ( th -> ta ) ) )
2		ee13.1	. . 3 |- ( ph -> ps )
3		ee13.3	. . 3 |- ( ps -> ( ta -> et ) )
4	2, 3	syl 17	. 2 |- ( ph -> ( ta -> et ) )
5	1, 4	syl6d 75	1 |- ( ph -> ( ch -> ( th -> et ) ) )

Syntax hints:   -> wi 4

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

This theorem is referenced by:  sbcim2g  38748  ee13an  38977