Theorem bj-drnf2v

Description: Version of drnf2 with a disjoint variable condition, which does not require ax-10 , ax-11 , ax-12 , ax-13 . Instance of nfbidv . Note that the version of axc15 with a disjoint variable condition is actually ax12v2 (up to adding a superfluous antecedent). (Contributed by BJ, 17-Jun-2019) (Proof modification is discouraged.)

	Ref	Expression
Hypothesis	bj-drnf2v.1	$$⊢\forall xx=y\to \left(\phi \leftrightarrow \psi \right)$$
Assertion	bj-drnf2v	$$⊢\forall xx=y\to \left(Ⅎz\phi \leftrightarrow Ⅎz\psi \right)$$

Proof

Step	Hyp	Ref	Expression
1		bj-drnf2v.1	$$⊢\forall xx=y\to \left(\phi \leftrightarrow \psi \right)$$
2	1	nfbidv	$$⊢\forall xx=y\to \left(Ⅎz\phi \leftrightarrow Ⅎz\psi \right)$$