Theorem mo4OLD

Description: Obsolete version of mo4 as of 18-Oct-2023. (Contributed by NM, 26-Jul-1995) (New usage is discouraged.) (Proof modification is discouraged.)

	Ref	Expression
Hypothesis	mo4OLD.1	$$⊢x=y\to \left(\phi \leftrightarrow \psi \right)$$
Assertion	mo4OLD	$$⊢{\exists }^{*}x\phi \leftrightarrow \forall x\forall y\left(\left(\phi \wedge \psi \right)\to x=y\right)$$

Proof

Step	Hyp	Ref	Expression
1		mo4OLD.1	$$⊢x=y\to \left(\phi \leftrightarrow \psi \right)$$
2		nfv	$$⊢Ⅎx\psi$$
3	2 1	mo4f	$$⊢{\exists }^{*}x\phi \leftrightarrow \forall x\forall y\left(\left(\phi \wedge \psi \right)\to x=y\right)$$