Theorem ee30 38972

Description: e30 38971 without virtual deductions. (Contributed by Alan Sare, 17-Jul-2011.) (Proof modification is discouraged.) (New usage is discouraged.)

Hypotheses

Ref	Expression
ee30.1	|- ( ph -> ( ps -> ( ch -> th ) ) )
ee30.2	|- ta
ee30.3	|- ( th -> ( ta -> et ) )

Assertion

Ref	Expression
ee30	|- ( ph -> ( ps -> ( ch -> et ) ) )

Proof of Theorem ee30

Step	Hyp	Ref	Expression
1		ee30.1	. 2 |- ( ph -> ( ps -> ( ch -> th ) ) )
2		ee30.2	. . . . 5 |- ta
3	2	a1i 11	. . . 4 |- ( ch -> ta )
4	3	a1i 11	. . 3 |- ( ps -> ( ch -> ta ) )
5	4	a1i 11	. 2 |- ( ph -> ( ps -> ( ch -> ta ) ) )
6		ee30.3	. 2 |- ( th -> ( ta -> et ) )
7	1, 5, 6	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:  ee30an  38974