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Metamath Proof Explorer

Theorem dfsn2

Description: Alternate definition of singleton. Definition 5.1 of TakeutiZaring p. 15. (Contributed by NM, 24-Apr-1994)

Ref Expression
Assertion dfsn2 ⊢ A = A A

Proof

Step Hyp Ref Expression
1 df-pr ⊢ A A = A ∪ A
2 unidm ⊢ A ∪ A = A
3 1 2 eqtr2i ⊢ A = A A