Description: Alternate definition of the class of all singletons. (Contributed by Scott Fenton, 20-Nov-2013) (Revised by Mario Carneiro, 19-Apr-2014)
Ref | Expression | ||
---|---|---|---|
Assertion | dfsingles2 | ⊢ Singletons = { 𝑥 ∣ ∃ 𝑦 𝑥 = { 𝑦 } } |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | elsingles | ⊢ ( 𝑥 ∈ Singletons ↔ ∃ 𝑦 𝑥 = { 𝑦 } ) | |
2 | 1 | abbi2i | ⊢ Singletons = { 𝑥 ∣ ∃ 𝑦 𝑥 = { 𝑦 } } |