Theorem reximdai

Description: Deduction from Theorem 19.22 of Margaris p. 90. (Restricted quantifier version.) (Contributed by NM, 31-Aug-1999)

	Ref	Expression
Hypotheses	reximdai.1	|- F/ x ph
	reximdai.2	|- ( ph -> ( x e. A -> ( ps -> ch ) ) )
Assertion	reximdai	|- ( ph -> ( E. x e. A ps -> E. x e. A ch ) )

Proof

Step	Hyp	Ref	Expression
1		reximdai.1	|- F/ x ph
2		reximdai.2	|- ( ph -> ( x e. A -> ( ps -> ch ) ) )
3	1 2	ralrimi	|- ( ph -> A. x e. A ( ps -> ch ) )
4		rexim	|- ( A. x e. A ( ps -> ch ) -> ( E. x e. A ps -> E. x e. A ch ) )
5	3 4	syl	|- ( ph -> ( E. x e. A ps -> E. x e. A ch ) )