Theorem rexlimd3

Description: * Inference from Theorem 19.23 of Margaris p. 90 (restricted quantifier version). (Contributed by Glauco Siliprandi, 2-Jan-2022)

	Ref	Expression
Hypotheses	rexlimd3.1	|- F/ x ph
	rexlimd3.2	|- F/ x ch
	rexlimd3.3	|- ( ( ( ph /\ x e. A ) /\ ps ) -> ch )
Assertion	rexlimd3	|- ( ph -> ( E. x e. A ps -> ch ) )

Proof

Step	Hyp	Ref	Expression
1		rexlimd3.1	|- F/ x ph
2		rexlimd3.2	|- F/ x ch
3		rexlimd3.3	|- ( ( ( ph /\ x e. A ) /\ ps ) -> ch )
4	3	exp31	|- ( ph -> ( x e. A -> ( ps -> ch ) ) )
5	1 2 4	rexlimd	|- ( ph -> ( E. x e. A ps -> ch ) )