A sufficient condition for a convex body to lie completely inside another convex body?

Question

Suppose we have two convex bodies in 3D space. Let’s call them $B_1$ and $B_2$. Let’s denote their projection curves on the xy plane by: $P_{1xy}$ and $P_{2xy}$, on the yz plane by: $P_{1yz}$ and $P_{2yz}$, on the zx plane by: $P_{1zx}$ and $P_{2zx}$.

Suppose the following three conditions are met:

1. $P_{2xy}$ lies completely inside $P_{1xy}$.
2. $P_{2yz}$ lies completely inside $P_{1yz}$.
3. $P_{2zx}$ lies completely inside $P_{1zx}$.

Are these conditions sufficient to say that B2 lies completely inside B1?

Thank you!