Theorem cbvalv

Rule used to change bound variables, using implicit substitution. Usage of this theorem is discouraged because it depends on [ax-13]. See cbvalvw for a version requiring fewer axioms, to be preferred when sufficient. (Contributed by NM, 5-Aug-1993.) Remove dependency on [ax-10] and shorten proof. (Revised by Wolf Lammen, 11-Sep-2023.) (New usage is discouraged.)

Hypothesis
cbvalv.1
\( \vdash x = y \rightarrow (\varphi \leftrightarrow \psi) \)
Conclusion
\( \vdash \forall x \, \varphi \leftrightarrow \forall y \, \psi \)
Proof
l0
nfv
l1
nfv
cbvalv.1
cbval l0 l1 _