Theorem aecom

Description: Commutation law for identical variable specifiers. Both sides of the biconditional are true when x and y are substituted with the same variable. Usage of this theorem is discouraged because it depends on ax-13 . (Contributed by NM, 10-May-1993) Change to a biconditional. (Revised by BJ, 26-Sep-2019) (New usage is discouraged.)

	Ref	Expression
Assertion	aecom	$$⊢\forall xx=y\leftrightarrow \forall yy=x$$

Proof

Step	Hyp	Ref	Expression
1		axc11n	$$⊢\forall xx=y\to \forall yy=x$$
2		axc11n	$$⊢\forall yy=x\to \forall xx=y$$
3	1 2	impbii	$$⊢\forall xx=y\leftrightarrow \forall yy=x$$