Theorem eqimssd

Description: Equality implies inclusion, deduction version. (Contributed by SN, 6-Nov-2024)

	Ref	Expression
Hypothesis	eqimssd.1	⊢ ( 𝜑 → 𝐴 = 𝐵 )
Assertion	eqimssd	⊢ ( 𝜑 → 𝐴 ⊆ 𝐵 )

Proof

Step	Hyp	Ref	Expression
1		eqimssd.1	⊢ ( 𝜑 → 𝐴 = 𝐵 )
2		ssid	⊢ 𝐵 ⊆ 𝐵
3	1 2	eqsstrdi	⊢ ( 𝜑 → 𝐴 ⊆ 𝐵 )