Description: A set is identical to itself. (Contributed by NM, 28-May-2008) (Proof shortened by Andrew Salmon, 27-Aug-2011)
Ref | Expression | ||
---|---|---|---|
Assertion | ididg | ⊢ ( 𝐴 ∈ 𝑉 → 𝐴 I 𝐴 ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | eqid | ⊢ 𝐴 = 𝐴 | |
2 | ideqg | ⊢ ( 𝐴 ∈ 𝑉 → ( 𝐴 I 𝐴 ↔ 𝐴 = 𝐴 ) ) | |
3 | 1 2 | mpbiri | ⊢ ( 𝐴 ∈ 𝑉 → 𝐴 I 𝐴 ) |