Theorem ee31 38979

Description: e31 38978 without virtual deductions. (Contributed by Alan Sare, 25-Jul-2011.) (Proof modification is discouraged.) (New usage is discouraged.)

Hypotheses

Ref	Expression
ee31.1	|- ( ph -> ( ps -> ( ch -> th ) ) )
ee31.2	|- ( ph -> ta )
ee31.3	|- ( th -> ( ta -> et ) )

Assertion

Ref	Expression
ee31	|- ( ph -> ( ps -> ( ch -> et ) ) )

Proof of Theorem ee31

Step	Hyp	Ref	Expression
1		ee31.1	. 2 |- ( ph -> ( ps -> ( ch -> th ) ) )
2		ee31.2	. . . 4 |- ( ph -> ta )
3	2	a1d 25	. . 3 |- ( ph -> ( ch -> ta ) )
4	3	a1d 25	. 2 |- ( ph -> ( ps -> ( ch -> ta ) ) )
5		ee31.3	. 2 |- ( th -> ( ta -> et ) )
6	1, 4, 5	ee33 38727	1 |- ( ph -> ( ps -> ( ch -> 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:  trintALT  39117