This statement is not completely correct for a firm in perfect competition. Instead, all of these things should be equal to one another. In other words, there should be no inequalities here. You could simply rewrite the statement with all of the “greater than” signs being changed to “equals” signs.
The most important clue that allows us to know that the statement that was given in the question is incorrect is the fact that marginal revenue and marginal cost are not equal in that statement. In perfect competition (as in all market structures) profit is maximized at a point where marginal revenues and marginal costs are equal. Therefore, there can be no long term equilibrium unless these two are equal.
All of the other costs are also equal to marginal revenue and to price as well. For a full explanation of why this is (which would be much too long for our space here), follow this link.