# Multiplication by Negative Real Number/Corollary

## Corollary to Multiplication by Negative Real Number

$\forall x \in \R: \paren {-1} \times x = -x$

## Proof

 $\displaystyle \paren {-1} \times x$ $=$ $\displaystyle -\paren {1 \times x}$ Multiplication by Negative Real Number $\displaystyle$ $=$ $\displaystyle -x$ Real Number Axioms: $\R M 3$: Identity for Multiplication

$\blacksquare$