Is AR(1)-ARCH(1) covariance stationary? And why?

[A_Jo]

I'm becoming confused by this. Say I have the following model:

y_t = c + ϕy_{t−1} + ϵ_t, ϵ_t|Ω_{t−1} ~ WN(0,σ^2_t)
σ^2_t = α_0 + α_1 + ϵ^2_{t−1}
|ϕ|<1, α_1<1, α_0≥0, α1>0.

I know that an AR(1) is covariance stationary if |ϕ|<1.
I also know that an ARCH(1) is covariance stationary if α_0>0, α_1>0 and α1<1 .

If those conditions hold does that imply that an AR(1)-ARCH(1) is also covariance stationary?