Theorem 19.3v

Description: Version of 19.3 with a disjoint variable condition, requiring fewer axioms. Any formula can be universally quantified using a variable which it does not contain. See also 19.9v . (Contributed by Anthony Hart, 13-Sep-2011) Remove dependency on ax-7 . (Revised by Wolf Lammen, 4-Dec-2017) (Proof shortened by Wolf Lammen, 20-Oct-2023)

	Ref	Expression
Assertion	19.3v	$$⊢\forall x\phi \leftrightarrow \phi$$

Proof

Step	Hyp	Ref	Expression
1		spvw	$$⊢\forall x\phi \to \phi$$
2		ax-5	$$⊢\phi \to \forall x\phi$$
3	1 2	impbii	$$⊢\forall x\phi \leftrightarrow \phi$$