Theorem eqimss

Description: Equality implies inclusion. (Contributed by NM, 21-Jun-1993) (Proof shortened by Andrew Salmon, 21-Jun-2011)

	Ref	Expression
Assertion	eqimss	⊢ ( 𝐴 = 𝐵 → 𝐴 ⊆ 𝐵 )

Proof

Step	Hyp	Ref	Expression
1		id	⊢ ( 𝐴 = 𝐵 → 𝐴 = 𝐵 )
2	1	eqimssd	⊢ ( 𝐴 = 𝐵 → 𝐴 ⊆ 𝐵 )