Theorem axc16gb

Description: Biconditional strengthening of axc16g . (Contributed by NM, 15-May-1993)

	Ref	Expression
Assertion	axc16gb	$$⊢\forall xx=y\to \left(\phi \leftrightarrow \forall z\phi \right)$$

Proof

Step	Hyp	Ref	Expression
1		axc16g	$$⊢\forall xx=y\to \left(\phi \to \forall z\phi \right)$$
2		sp	$$⊢\forall z\phi \to \phi$$
3	1 2	impbid1	$$⊢\forall xx=y\to \left(\phi \leftrightarrow \forall z\phi \right)$$