Theorem alrimdd

Description: Deduction form of Theorem 19.21 of Margaris p. 90, see 19.21 . (Contributed by Mario Carneiro, 24-Sep-2016)

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

Proof

Step	Hyp	Ref	Expression
1		alrimdd.1	|- F/ x ph
2		alrimdd.2	|- ( ph -> F/ x ps )
3		alrimdd.3	|- ( ph -> ( ps -> ch ) )
4	2	nf5rd	|- ( ph -> ( ps -> A. x ps ) )
5	1 3	alimd	|- ( ph -> ( A. x ps -> A. x ch ) )
6	4 5	syld	|- ( ph -> ( ps -> A. x ch ) )