Theorem raleleq

Description: All elements of a class are elements of a class equal to this class. (Contributed by AV, 30-Oct-2020)

	Ref	Expression
Assertion	raleleq	$$⊢A=B\to \forall x\in Ax\in B$$

Proof

Step	Hyp	Ref	Expression
1		eleq2	$$⊢A=B\to \left(x\in A\leftrightarrow x\in B\right)$$
2	1	biimpd	$$⊢A=B\to \left(x\in A\to x\in B\right)$$
3	2	ralrimiv	$$⊢A=B\to \forall x\in Ax\in B$$