Metamath Proof Explorer
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 ) |