Theorem eqeltrrid

Description: A membership and equality inference. (Contributed by NM, 4-Jan-2006)

	Ref	Expression
Hypotheses	eqeltrrid.1	⊢ 𝐵 = 𝐴
	eqeltrrid.2	⊢ ( 𝜑 → 𝐵 ∈ 𝐶 )
Assertion	eqeltrrid	⊢ ( 𝜑 → 𝐴 ∈ 𝐶 )

Proof

Step	Hyp	Ref	Expression
1		eqeltrrid.1	⊢ 𝐵 = 𝐴
2		eqeltrrid.2	⊢ ( 𝜑 → 𝐵 ∈ 𝐶 )
3	1	eqcomi	⊢ 𝐴 = 𝐵
4	3 2	eqeltrid	⊢ ( 𝜑 → 𝐴 ∈ 𝐶 )