Theorem axc11rv

Description: Version of axc11r with a disjoint variable condition on x and y , which is provable, on top of { ax-1 -- ax-7 }, from ax12v (contrary to axc11 which seems to require the full ax-12 and ax-13 , and to axc11r which seems to require the full ax-12 ). (Contributed by BJ, 6-Jul-2021) (Proof shortened by Wolf Lammen, 11-Oct-2021)

	Ref	Expression
Assertion	axc11rv	$$⊢\forall xx=y\to \left(\forall y\phi \to \forall x\phi \right)$$

Proof

Step	Hyp	Ref	Expression
1		axc16	$$⊢\forall xx=y\to \left(\phi \to \forall x\phi \right)$$
2	1	spsd	$$⊢\forall xx=y\to \left(\forall y\phi \to \forall x\phi \right)$$