$n$ out of $ m$ theorems (some imply the rest) Is there symbolism (or even a name) for groups of statements in which any fixed-number of them imply all the rest?
For example, in linear algebra, a basis is sometimes defined as a set of n-dimensional vectors which:


*

*Is linearly independent

*Spans the vector space

*Contains exactly n elements


However, it is then shown that any TWO of these statements being true implies the third is true.  How would you write this symbolically? (other than $A \wedge B \Rightarrow C, A \wedge C \Rightarrow B, B \wedge C \Rightarrow A$, which does not scale well...)

Often the most obvious solution is the best solution. I would write T(s) be 1 if a statement is true and 0 if it is false. I would then call the statements A, B and C and let S={A, B, C}. Then is would write sum T(s) over S >=2 => all s are true. You can make these statement more symbolic if you really like
