Theorem albid

Description: Formula-building rule for universal quantifier (deduction form). (Contributed by Mario Carneiro, 24-Sep-2016)

	Ref	Expression
Hypotheses	albid.1	$$⊢Ⅎx\phi$$
	albid.2	$$⊢\phi \to \left(\psi \leftrightarrow \chi \right)$$
Assertion	albid	$$⊢\phi \to \left(\forall x\psi \leftrightarrow \forall x\chi \right)$$

Proof

Step	Hyp	Ref	Expression
1		albid.1	$$⊢Ⅎx\phi$$
2		albid.2	$$⊢\phi \to \left(\psi \leftrightarrow \chi \right)$$
3	1	nf5ri	$$⊢\phi \to \forall x\phi$$
4	3 2	albidh	$$⊢\phi \to \left(\forall x\psi \leftrightarrow \forall x\chi \right)$$