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Metamath Proof Explorer

Theorem 0ss

Description: The null set is a subset of any class. Part of Exercise 1 of TakeutiZaring p. 22. (Contributed by NM, 21-Jun-1993)

Ref Expression
Assertion 0ss ⊢ ∅ ⊆ A

Proof

Step Hyp Ref Expression
1 noel ⊢ ¬ x ∈ ∅
2 1 pm2.21i ⊢ x ∈ ∅ → x ∈ A
3 2 ssriv ⊢ ∅ ⊆ A