Theorem rexlimddv2

Description: Restricted existential elimination rule of natural deduction. (Contributed by Glauco Siliprandi, 5-Feb-2022)

	Ref	Expression
Hypotheses	rexlimddv2.1	|- ( ph -> E. x e. A ps )
	rexlimddv2.2	|- ( ( ( ph /\ x e. A ) /\ ps ) -> ch )
Assertion	rexlimddv2	|- ( ph -> ch )

Proof

Step	Hyp	Ref	Expression
1		rexlimddv2.1	|- ( ph -> E. x e. A ps )
2		rexlimddv2.2	|- ( ( ( ph /\ x e. A ) /\ ps ) -> ch )
3	2	anasss	|- ( ( ph /\ ( x e. A /\ ps ) ) -> ch )
4	1 3	rexlimddv	|- ( ph -> ch )