Theorem naecoms-o

Description: A commutation rule for distinct variable specifiers. Version of naecoms using ax-c11 . (Contributed by NM, 2-Jan-2002) (Proof modification is discouraged.) (New usage is discouraged.)

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

Proof

Step	Hyp	Ref	Expression
1		nalequcoms-o.1	$$⊢\neg \forall xx=y\to \phi$$
2		aecom-o	$$⊢\forall xx=y\to \forall yy=x$$
3	2 1	nsyl4	$$⊢\neg \phi \to \forall yy=x$$
4	3	con1i	$$⊢\neg \forall yy=x\to \phi$$