Theorem axc16b

Description: This theorem shows that axiom ax-c16 is redundant in the presence of theorem dtru , which states simply that at least two things exist. This justifies the remark at mmzfcnd.html#twoness (which links to this theorem). (Proof modification is discouraged.) (New usage is discouraged.) (Contributed by NM, 7-Nov-2006)

	Ref	Expression
Assertion	axc16b	|- ( A. x x = y -> ( ph -> A. x ph ) )

Proof

Step	Hyp	Ref	Expression
1		dtru	|- -. A. x x = y
2	1	pm2.21i	|- ( A. x x = y -> ( ph -> A. x ph ) )