In the Hebrew wiki page on Nash equilibrium there is a reference to an indifference principle which means that once we know the other player uses the equilibrium strategy then the first player can use any pure strategy with positive probability in his equilibrium strategy and get the same payoff as the optimal one.
What's the English term?
You are referring to a result due to Nash himself (work published in the late $40$s -- early $50$s), which is now loosely known as the indifference principle / theorem in mainstream literature. This result basically states that for a matrix game (specified by a payoff matrix $A \in \mathbb{R}^{n_1 \times n_2}$ and an $n_k$-dimensional probability simplex $\Delta_k$ for player $k \in \{1, 2\}$) , given a strategy $y_0 \in \Delta_2$ for player (the "min" player, then any best response strategy $x \in \Delta_1$ for player 1 (the "max" player) has the following (indifference) property: if the $i$ component of $x_0$ is nonzero, then $i$th pure strategy (a kink of $\Delta_2$) is also a best response strategy, i.e $(Ay_0)_i = x_0^TAy_0 = \max_{x \in \Delta_1}x^TAy_0$.
The above result simply says that the maximum of a linear function on a simplex is attained at a kink.