Theorem bj-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) State the most general derivable instance. (Revised by BJ, 5-Apr-2026)

	Ref	Expression
Hypotheses	bj-alrimdh.nf1	|- ( ph -> A. x ps )
	bj-alrimdh.nf2	|- ( ch -> A. x th )
	bj-alrimdh.maj	|- ( ps -> ( th -> ta ) )
Assertion	bj-alrimdh	|- ( ph -> ( ch -> A. x ta ) )

Proof

Step	Hyp	Ref	Expression
1		bj-alrimdh.nf1	|- ( ph -> A. x ps )
2		bj-alrimdh.nf2	|- ( ch -> A. x th )
3		bj-alrimdh.maj	|- ( ps -> ( th -> ta ) )
4	1 3	bj-alimdh	|- ( ph -> ( A. x th -> A. x ta ) )
5	2 4	syl5	|- ( ph -> ( ch -> A. x ta ) )