Metamath Proof Explorer


Theorem brssrid

Description: Any set is a subset of itself. (Contributed by Peter Mazsa, 1-Aug-2019)

Ref Expression
Assertion brssrid ( 𝐴 ∈ 𝑉 → 𝐴 S 𝐴 )

Proof

Step Hyp Ref Expression
1 ssid ⊢ 𝐴 ⊆ 𝐴
2 brssr ⊢ ( 𝐴 ∈ 𝑉 → ( 𝐴 S 𝐴 ↔ 𝐴 ⊆ 𝐴 ) )
3 1 2 mpbiri ⊢ ( 𝐴 ∈ 𝑉 → 𝐴 S 𝐴 )