Theorem bj-notalbii

Description: Equivalence of universal quantification of negation of equivalent formulas. Shortens ab0 (103>94), ballotlem2 (2655>2648), bnj1143 (522>519), hausdiag (2119>2104). (Contributed by BJ, 17-Jul-2021)

	Ref	Expression
Hypothesis	bj-notalbii.1	$$⊢\phi \leftrightarrow \psi$$
Assertion	bj-notalbii	$$⊢\forall x\neg \phi \leftrightarrow \forall x\neg \psi$$

Proof

Step	Hyp	Ref	Expression
1		bj-notalbii.1	$$⊢\phi \leftrightarrow \psi$$
2	1	notbii	$$⊢\neg \phi \leftrightarrow \neg \psi$$
3	2	albii	$$⊢\forall x\neg \phi \leftrightarrow \forall x\neg \psi$$