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