Theorem eqimsscd

Description: Equality implies inclusion, deduction version. (Contributed by SN, 15-Feb-2025)

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

Proof

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