Theorem nfabdOLD

Description: Obsolete version of nfabd as of 10-May-2023. (Contributed by Mario Carneiro, 8-Oct-2016) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Hypotheses	nfabdOLD.1	$$⊢Ⅎy\phi$$
	nfabdOLD.2	$$⊢\phi \to Ⅎx\psi$$
Assertion	nfabdOLD	$$⊢\phi \to \underset{\_}{Ⅎ}x\left\{y|\psi \right\}$$

Proof

Step	Hyp	Ref	Expression
1		nfabdOLD.1	$$⊢Ⅎy\phi$$
2		nfabdOLD.2	$$⊢\phi \to Ⅎx\psi$$
3	2	adantr	$$⊢\left(\phi \wedge \neg \forall xx=y\right)\to Ⅎx\psi$$
4	1 3	nfabd2	$$⊢\phi \to \underset{\_}{Ⅎ}x\left\{y|\psi \right\}$$