Theorem naecoms

Description: A commutation rule for distinct variable specifiers. Usage of this theorem is discouraged because it depends on ax-13 . (Contributed by NM, 2-Jan-2002) (New usage is discouraged.)

	Ref	Expression
Hypothesis	naecoms.1	$$⊢\neg \forall xx=y\to \phi$$
Assertion	naecoms	$$⊢\neg \forall yy=x\to \phi$$

Proof

Step	Hyp	Ref	Expression
1		naecoms.1	$$⊢\neg \forall xx=y\to \phi$$
2		aecom	$$⊢\forall xx=y\leftrightarrow \forall yy=x$$
3	2 1	sylnbir	$$⊢\neg \forall yy=x\to \phi$$