Sentence examples for the following implications from inspiring English sources

Remark 2.1 It follows from the proof of the above theorems that the following implications hold: Theorem 2.1 ⟹ Theorem 2.2 ⟹Theorem 2.3 ⟹ Theorem 2.4.

Note also that the following implications hold.

The inequality presented in Eq. 21 has the following implications.

In general, the following implications hold: T polaroid ⇒ T isoloid.

Does either of the following implications for a Banach space X hold?

Conversely, it is clear that the following implications hold: Theorem 2.4 ⟹ Theorem 2.3 ⟹ Theorem 2.2.

The following implication holds: (3.23).

For the following implication holds: (1.6).

(i) For the following implication holds:  .

The following implication holds: the (WBCQ) ⟹ the quasi (WBCQ).

Thus, we must conclude that the following implication holds (4.7).