From my understanding these two statements are logically equivalent

p → q ≡∼p ∨ q (can someone 'explainlikei'mfive' why that makes sense)

When I come across this, 

(∀a)(∀b)(∃c)[a < b → a < c < b]

is it the same as

(∀a)(∀b)(∃c)[a ≥ b ∨ (a < c < b)]