Theorem bj-axc11v

Description: Version of axc11 with a disjoint variable condition, which does not require ax-13 nor ax-10 . Remark: the following theorems ( hbae , nfae , hbnae , nfnae , hbnaes ) would need to be totally unbundled to be proved without ax-13 , hence would be simple consequences of ax-5 or nfv . (Contributed by BJ, 31-May-2019) (Proof modification is discouraged.)

	Ref	Expression
Assertion	bj-axc11v	$$⊢\forall xx=y\to \left(\forall x\phi \to \forall y\phi \right)$$

Proof

Step	Hyp	Ref	Expression
1		axc11rv	$$⊢\forall yy=x\to \left(\forall x\phi \to \forall y\phi \right)$$
2	1	bj-aecomsv	$$⊢\forall xx=y\to \left(\forall x\phi \to \forall y\phi \right)$$