Theorem dral2-o

Description: Formula-building lemma for use with the Distinctor Reduction Theorem. Part of Theorem 9.4 of Megill p. 448 (p. 16 of preprint). Version of dral2 using ax-c11 . (Contributed by NM, 27-Feb-2005) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Hypothesis	dral2-o.1	$$⊢\forall xx=y\to \left(\phi \leftrightarrow \psi \right)$$
Assertion	dral2-o	$$⊢\forall xx=y\to \left(\forall z\phi \leftrightarrow \forall z\psi \right)$$

Proof

Step	Hyp	Ref	Expression
1		dral2-o.1	$$⊢\forall xx=y\to \left(\phi \leftrightarrow \psi \right)$$
2		hbae-o	$$⊢\forall xx=y\to \forall z\forall xx=y$$
3	2 1	albidh	$$⊢\forall xx=y\to \left(\forall z\phi \leftrightarrow \forall z\psi \right)$$