Theorem axc16b

Description: This theorem shows that Axiom ax-c16 is redundant in the presence of Theorem dtruALT2 , 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	$$⊢\forall xx=y\to \left(\phi \to \forall x\phi \right)$$

Proof

Step	Hyp	Ref	Expression
1		dtruALT2	$$⊢\neg \forall xx=y$$
2	1	pm2.21i	$$⊢\forall xx=y\to \left(\phi \to \forall x\phi \right)$$