Theorem ab0orvALT

Description: Alternate proof of ab0orv , shorter but using more axioms. (Contributed by Mario Carneiro, 29-Aug-2013) (Revised by BJ, 22-Mar-2020) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Assertion	ab0orvALT	$$⊢\left(\left\{x|\phi \right\}=\mathrm{V}\vee \left\{x|\phi \right\}=\varnothing \right)$$

Proof

Step	Hyp	Ref	Expression
1		nfv	$$⊢Ⅎx\phi$$
2		dfnf5	$$⊢Ⅎx\phi \leftrightarrow \left(\left\{x|\phi \right\}=\mathrm{V}\vee \left\{x|\phi \right\}=\varnothing \right)$$
3	1 2	mpbi	$$⊢\left(\left\{x|\phi \right\}=\mathrm{V}\vee \left\{x|\phi \right\}=\varnothing \right)$$