Theorem sb9i

Description: Commutation of quantification and substitution variables. Usage of this theorem is discouraged because it depends on ax-13 . (Contributed by NM, 5-Aug-1993) (Proof shortened by Wolf Lammen, 15-Jun-2019) (New usage is discouraged.)

	Ref	Expression
Assertion	sb9i	$$⊢\forall x\left[x/y\right]\phi \to \forall y\left[y/x\right]\phi$$

Proof

Step	Hyp	Ref	Expression
1		sb9	$$⊢\forall x\left[x/y\right]\phi \leftrightarrow \forall y\left[y/x\right]\phi$$
2	1	biimpi	$$⊢\forall x\left[x/y\right]\phi \to \forall y\left[y/x\right]\phi$$