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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 C_ (/) -> A = (/) )

Proof

Step Hyp Ref Expression
1 ss0b 
 |-  ( A C_ (/) <-> A = (/) )
2 1 biimpi 
 |-  ( A C_ (/) -> A = (/) )