Theorem ss0

Description: Any subset of the empty set is empty. Theorem 5 of Suppes p. 23. (Contributed by NM, 13-Aug-1994)

	Ref	Expression
Assertion	ss0	⊢ ( 𝐴 ⊆ ∅ → 𝐴 = ∅ )

Proof

Step	Hyp	Ref	Expression
1		ss0b	⊢ ( 𝐴 ⊆ ∅ ↔ 𝐴 = ∅ )
2	1	biimpi	⊢ ( 𝐴 ⊆ ∅ → 𝐴 = ∅ )