contrary to ...
Contrary to the doctor's advice, he had gone back to work
Contrary to all expectations
on the contrary;  conversely;  inversely;  contrariwise
It isn't useless to me, on the contrary,  I think it's rather useful
Conversely, we could conclude that ...
vice versa
I put the wardrobe where the bed was and vice versa
What is white here is black over there and vice versa
to the contrary;  otherwise
The meeting will be at six, unless otherwise informed;  The meeting will be at six, unless you hear to the contrary
To produce proof to the contrary
inverse;  reverse;  opposite
I take the opposite view
In the opposite/reverse direction
In inverse/reverse order
But the reverse/contrary isn't true