Theorem 0npr

Description: The empty set is not a positive real. (Contributed by NM, 15-Nov-1995) (New usage is discouraged.)

	Ref	Expression
Assertion	0npr	⊢ ¬ ∅ ∈ P

Proof

Step	Hyp	Ref	Expression
1		eqid	⊢ ∅ = ∅
2		prn0	⊢ ( ∅ ∈ P → ∅ ≠ ∅ )
3	2	necon2bi	⊢ ( ∅ = ∅ → ¬ ∅ ∈ P )
4	1 3	ax-mp	⊢ ¬ ∅ ∈ P