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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 )

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 )