Rule of Association/Disjunction

Theorem

Disjunction is associative:

Formulation 1

$p \lor \paren {q \lor r} \dashv \vdash \paren {p \lor q} \lor r$

Formulation 2

$\vdash \paren {p \lor \paren {q \lor r} } \iff \paren {\paren {p \lor q} \lor r}$

Also see

• Rule of Commutation

Sources

• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): or
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): or