Theorem equs3OLD

Description: Obsolete as of 12-Aug-2023. Use alinexa or sbn instead. Lemma used in proofs of substitution properties. (Contributed by NM, 10-May-1993) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Assertion	equs3OLD	$$⊢\exists x\left(x=y\wedge \phi \right)\leftrightarrow \neg \forall x\left(x=y\to \neg \phi \right)$$

Proof

Step	Hyp	Ref	Expression
1		alinexa	$$⊢\forall x\left(x=y\to \neg \phi \right)\leftrightarrow \neg \exists x\left(x=y\wedge \phi \right)$$
2	1	con2bii	$$⊢\exists x\left(x=y\wedge \phi \right)\leftrightarrow \neg \forall x\left(x=y\to \neg \phi \right)$$