continuous signals - Fourier Transform Identities

We know the below,

$$\mathscr{F}\big\{x(t)\big\}=X(f) \tag{1}$$ $$\mathscr{F}\big\{x(-t)\big\}=X(-f) \tag{2}$$ $$\mathscr{F}\big\{x^*(t)\big\}=X^*(-f) \tag{3}$$

Now, if for some signal

$$x(-t)=x^*(t) \tag{4}$$

Then, is it safe to assume the following?

$$X(-f)=X^*(-f) \tag{5}$$

or does it depend on the type of signal?