Theorem eubiOLD

Description: Obsolete proof of eubi as of 7-Oct-2022. (Contributed by Andrew Salmon, 11-Jul-2011) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Assertion	eubiOLD	$$⊢\forall x\left(\phi \leftrightarrow \psi \right)\to \left(\exists !x\phi \leftrightarrow \exists !x\psi \right)$$

Proof

Step	Hyp	Ref	Expression
1		nfa1	$$⊢Ⅎx\forall x\left(\phi \leftrightarrow \psi \right)$$
2		sp	$$⊢\forall x\left(\phi \leftrightarrow \psi \right)\to \left(\phi \leftrightarrow \psi \right)$$
3	1 2	eubid	$$⊢\forall x\left(\phi \leftrightarrow \psi \right)\to \left(\exists !x\phi \leftrightarrow \exists !x\psi \right)$$