Theorem ee32an

Description: e33an without virtual deductions. (Contributed by Alan Sare, 14-Jul-2011) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Hypotheses	ee32an.1	|- ( ph -> ( ps -> ( ch -> th ) ) )
	ee32an.2	|- ( ph -> ( ps -> ta ) )
	ee32an.3	|- ( ( th /\ ta ) -> et )
Assertion	ee32an	|- ( ph -> ( ps -> ( ch -> et ) ) )

Proof

Step	Hyp	Ref	Expression
1		ee32an.1	|- ( ph -> ( ps -> ( ch -> th ) ) )
2		ee32an.2	|- ( ph -> ( ps -> ta ) )
3		ee32an.3	|- ( ( th /\ ta ) -> et )
4	2	a1dd	|- ( ph -> ( ps -> ( ch -> ta ) ) )
5	1 4 3	ee33an	|- ( ph -> ( ps -> ( ch -> et ) ) )