Theorem ralsd

Description: Introduction rule for "all some" restricted to a class. This is the converse of rals1d and rals2d taken together. (Contributed by David A. Wheeler, 12-Jul-2026)

	Ref	Expression
Hypotheses	ralsd.1	$$⊢\phi \to \forall x\in A\left(\psi \to \chi \right)$$
	ralsd.2	$$⊢\phi \to \exists x\in A\psi$$
Assertion	ralsd	Could not format assertion : No typesetting found for |- ( ph -> AE x e. A ( ps -> ch ) ) with typecode |-

Proof

Step	Hyp	Ref	Expression
1		ralsd.1	$$⊢\phi \to \forall x\in A\left(\psi \to \chi \right)$$
2		ralsd.2	$$⊢\phi \to \exists x\in A\psi$$
3		df-rals	Could not format ( AE x e. A ( ps -> ch ) <-> ( A. x e. A ( ps -> ch ) /\ E. x e. A ps ) ) : No typesetting found for |- ( AE x e. A ( ps -> ch ) <-> ( A. x e. A ( ps -> ch ) /\ E. x e. A ps ) ) with typecode |-
4	1 2 3	sylanbrc	Could not format ( ph -> AE x e. A ( ps -> ch ) ) : No typesetting found for |- ( ph -> AE x e. A ( ps -> ch ) ) with typecode |-