Theorem cbval2vv

Rule used to change bound variables, using implicit substitution. Usage of this theorem is discouraged because it depends on [ax-13]. Use the weaker cbval2vw if possible. (Contributed by NM, 4-Feb-2005.) Remove dependency on [ax-10]. (Revised by Wolf Lammen, 18-Jul-2021.) (New usage is discouraged.)

Hypothesis

cbval2vv.1

\( \vdash x = z \wedge y = w \rightarrow (\varphi \leftrightarrow \psi) \)

Conclusion

\( \vdash \forall x \, \forall y \, \varphi \leftrightarrow \forall z \, \forall w \, \psi \)

Proof

cbval2vv.1

cbvaldva _

cbvalv _