Theorem sbbibvv

Description: Reversal of substitution. (Contributed by AV, 6-Aug-2023)

	Ref	Expression
Assertion	sbbibvv	$$⊢\forall y\left(\left[y/x\right]\phi \leftrightarrow \psi \right)\leftrightarrow \forall x\left(\phi \leftrightarrow \left[x/y\right]\psi \right)$$

Proof

Step	Hyp	Ref	Expression
1		nfv	$$⊢Ⅎy\phi$$
2		nfv	$$⊢Ⅎx\psi$$
3	1 2	sbbib	$$⊢\forall y\left(\left[y/x\right]\phi \leftrightarrow \psi \right)\leftrightarrow \forall x\left(\phi \leftrightarrow \left[x/y\right]\psi \right)$$