Theorem alrimdh

Description: Deduction form of Theorem 19.21 of Margaris p. 90, see 19.21 and 19.21h . (Contributed by NM, 10-Feb-1997) (Proof shortened by Andrew Salmon, 13-May-2011)

	Ref	Expression
Hypotheses	alrimdh.1	|- ( ph -> A. x ph )
	alrimdh.2	|- ( ps -> A. x ps )
	alrimdh.3	|- ( ph -> ( ps -> ch ) )
Assertion	alrimdh	|- ( ph -> ( ps -> A. x ch ) )

Proof

Step	Hyp	Ref	Expression
1		alrimdh.1	|- ( ph -> A. x ph )
2		alrimdh.2	|- ( ps -> A. x ps )
3		alrimdh.3	|- ( ph -> ( ps -> ch ) )
4	1 3	alimdh	|- ( ph -> ( A. x ps -> A. x ch ) )
5	2 4	syl5	|- ( ph -> ( ps -> A. x ch ) )