Theorem drnf2

Description: Formula-building lemma for use with the Distinctor Reduction Theorem. (Contributed by Mario Carneiro, 4-Oct-2016) (Proof shortened by Wolf Lammen, 5-May-2018) Usage of this theorem is discouraged because it depends on ax-13 . Use nfbidv instead. (New usage is discouraged.)

	Ref	Expression
Hypothesis	dral1.1	$$⊢\forall xx=y\to \left(\phi \leftrightarrow \psi \right)$$
Assertion	drnf2	$$⊢\forall xx=y\to \left(Ⅎz\phi \leftrightarrow Ⅎz\psi \right)$$

Proof

Step	Hyp	Ref	Expression
1		dral1.1	$$⊢\forall xx=y\to \left(\phi \leftrightarrow \psi \right)$$
2		nfae	$$⊢Ⅎz\forall xx=y$$
3	2 1	nfbidf	$$⊢\forall xx=y\to \left(Ⅎz\phi \leftrightarrow Ⅎz\psi \right)$$