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Metamath Proof Explorer

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 = ∅ )