Theorem ee32 38986

Description: e32 38985 without virtual deductions. (Contributed by Alan Sare, 18-Jul-2011.) (Proof modification is discouraged.) (New usage is discouraged.)

Hypotheses

Ref	Expression
ee32.1	|- ( ph -> ( ps -> ( ch -> th ) ) )
ee32.2	|- ( ph -> ( ps -> ta ) )
ee32.3	|- ( th -> ( ta -> et ) )

Assertion

Ref	Expression
ee32	|- ( ph -> ( ps -> ( ch -> et ) ) )

Proof of Theorem ee32

Step	Hyp	Ref	Expression
1		ee32.1	. 2 |- ( ph -> ( ps -> ( ch -> th ) ) )
2		ee32.2	. . 3 |- ( ph -> ( ps -> ta ) )
3	2	a1dd 50	. 2 |- ( ph -> ( ps -> ( ch -> ta ) ) )
4		ee32.3	. 2 |- ( th -> ( ta -> et ) )
5	1, 3, 4	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: (None)