Theorem eleq1a

Description: A transitive-type law relating membership and equality. (Contributed by NM, 9-Apr-1994)

	Ref	Expression
Assertion	eleq1a	$$⊢A\in B\to \left(C=A\to C\in B\right)$$

Proof

Step	Hyp	Ref	Expression
1		eleq1	$$⊢C=A\to \left(C\in B\leftrightarrow A\in B\right)$$
2	1	biimprcd	$$⊢A\in B\to \left(C=A\to C\in B\right)$$