Commutativity of conjunction

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In logic, the commutativity of conjunction demonstrates that predicates on both sides of a logical conjunction operator are interchangeable. This logical law is a part of classical logic.

For any propositons 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 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.