I also thought like this, but still I have doubts:
If I replace ##p## with ##-p##, then instead of
##\displaystyle{\not} p = γ_μ p^μ = γ_0 p^0 +γ_i p^i##
I'll have
##\displaystyle{\not}p = γ_μ p^μ = γ_0 p^0 -γ_i p^i##.
But the last equation is not equal to ##-\displaystyle{\not}p## , because...