Theorem 3ralimi

Description: Inference quantifying both antecedent and consequent three times, with strong hypothesis. (Contributed by Scott Fenton, 5-Mar-2025)

	Ref	Expression
Hypothesis	2ralimi.1	$$⊢\phi \to \psi$$
Assertion	3ralimi	$$⊢\forall x\in A\forall y\in B\forall z\in C\phi \to \forall x\in A\forall y\in B\forall z\in C\psi$$

Proof

Step	Hyp	Ref	Expression
1		2ralimi.1	$$⊢\phi \to \psi$$
2	1	ralimi	$$⊢\forall z\in C\phi \to \forall z\in C\psi$$
3	2	2ralimi	$$⊢\forall x\in A\forall y\in B\forall z\in C\phi \to \forall x\in A\forall y\in B\forall z\in C\psi$$