In logic

Logic

In philosophy, Logic is the formal systematic study of the principles of valid inference and correct reasoning. Logic is used in most intellectual activities, but is studied primarily in the disciplines of philosophy, mathematics, semantics, and computer science...

, the commutativity of conjunction demonstrates that predicates on both sides of a logical conjunction

Logical conjunction

In logic and mathematics, a two-place logical operator and, also known as logical conjunction, results in true if both of its operands are true, otherwise the value of false....

 operator are interchangeable. This logical law is a part of classical logic

Classical logic

Classical logic identifies a class of formal logics that have been most intensively studied and most widely used. The class is sometimes called standard logic as well...

.

For any propositions H₁, H₂, ... H_n, and permutation σ(n) of the numbers 1 through n, it is the case that:

H₁ H₂ ... H_n

is equivalent to

H_σ(1) H_σ(2) H_σ(n).

For example, if H₁ is

It is raining

H₂ is

Socrates

Socrates

Socrates was a classical Greek Athenian philosopher. Credited as one of the founders of Western philosophy, he is an enigmatic figure known chiefly through the accounts of later classical writers, especially the writings of his students Plato and Xenophon, and the plays of his contemporary ...

is mortal

and H₃ is

2+2=4

then

It is raining and Socrates is mortal and 2+2=4

is equivalent to

Socrates is mortal and 2+2=4 and it is raining

and the other orderings of the predicates.
This law is also known as `and introduction' and is quite commonly abbreviated as `vI'.