Having trouble with some this proof
Prove that if a function is strictly increasing the function is injective.

A function is strictly increasing if $\forall x, \forall y, ((x < y) \implies (f(x) < f(y)))$

A function is injective if $\forall x, \forall y, ((f(x) = f(y) \implies (x = y))$

So to prove this implication my first goal was to transform all the implications into conjunctions then prove the contrapositive but it hasn't been fruitful.

I'll show what I have down.

$((x < y) \implies (f(x) < f(y))) \equiv \lnot (x < y) \lor (f(x) < f(y))$
$(x \geq y) \lor (f(x) < f(y)$


$((f(x) = f(y) \implies (x = y)) \equiv \lnot ((f(x) = f(y)) \lor (x = y)$