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, ... Hn, and permutation σ(n) of the numbers 1 through n, it is the case that:

H1 \land H2 \land ... \land Hn

is equivalent to

Hσ(1) \land Hσ(2) \land Hσ(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.

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