Theorem axc11

Description: Show that ax-c11 can be derived from ax-c11n in the form of axc11n . Normally, axc11 should be used rather than ax-c11 , except by theorems specifically studying the latter's properties. Usage of this theorem is discouraged because it depends on ax-13 . Use the weaker axc11v when possible. (Contributed by NM, 16-May-2008) (Proof shortened by Wolf Lammen, 21-Apr-2018) (New usage is discouraged.)

	Ref	Expression
Assertion	axc11	$$⊢\forall xx=y\to \left(\forall x\phi \to \forall y\phi \right)$$

Proof

Step	Hyp	Ref	Expression
1		axc11r	$$⊢\forall yy=x\to \left(\forall x\phi \to \forall y\phi \right)$$
2	1	aecoms	$$⊢\forall xx=y\to \left(\forall x\phi \to \forall y\phi \right)$$