Metamath Proof Explorer


Theorem snssd

Description: The singleton of an element of a class is a subset of the class (deduction form). (Contributed by Jonathan Ben-Naim, 3-Jun-2011)

Ref Expression
Hypothesis snssd.1 ⊢ ( 𝜑 → 𝐴 ∈ 𝐵 )
Assertion snssd ( 𝜑 → { 𝐴 } ⊆ 𝐵 )

Proof

Step Hyp Ref Expression
1 snssd.1 ⊢ ( 𝜑 → 𝐴 ∈ 𝐵 )
2 snssi ⊢ ( 𝐴 ∈ 𝐵 → { 𝐴 } ⊆ 𝐵 )
3 1 2 syl ⊢ ( 𝜑 → { 𝐴 } ⊆ 𝐵 )