Church-Rosser Theorem

This property of a reduction system states that if an expression can be reduced by zero or more reduction steps to either expression M or expression N then there exists some other expression to which both M and N can be reduced.

This implies that there is a unique normal form for any expression since M and N cannot be different normal forms because the theorem says they can be reduced to some other expression and normal forms are irreducible by definition.

It does not imply that a normal form is reachable, only that if reduction terminates it will reach a unique normal form.