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?