Theorem ee23an

Description: e23an without virtual deductions. (Contributed by Alan Sare, 14-Jul-2011) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Hypotheses	ee23an.1	|- ( ph -> ( ps -> ch ) )
	ee23an.2	|- ( ph -> ( ps -> ( th -> ta ) ) )
	ee23an.3	|- ( ( ch /\ ta ) -> et )
Assertion	ee23an	|- ( ph -> ( ps -> ( th -> et ) ) )

Proof

Step	Hyp	Ref	Expression
1		ee23an.1	|- ( ph -> ( ps -> ch ) )
2		ee23an.2	|- ( ph -> ( ps -> ( th -> ta ) ) )
3		ee23an.3	|- ( ( ch /\ ta ) -> et )
4	1	a1dd	|- ( ph -> ( ps -> ( th -> ch ) ) )
5	4 2 3	ee33an	|- ( ph -> ( ps -> ( th -> et ) ) )