Theorem 2ralimi

Description: Inference quantifying both antecedent and consequent two times, with strong hypothesis. (Contributed by AV, 3-Dec-2021)

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

Proof

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