The uniform subspace of X is identical with the uniform subspace

Question

If $ B\subseteq A\subseteq X $, then the uniform subspace $ B $ of $ X $ is identical with the uniform subspace $ B $ of the uniform subspace $ A $ of $ X $ ?

Answer 1

Immediate from $$U \cap (B \times B)= \left(U \cap (A \times A)\right) \cap (B \times B)$$ when $U$ is an entourage of $X$.