Let a, b, and c be real numbers.
If a = b, then a + c = b + c and c + a = c + b.
i.e. When two quantities are equal, if you add the same number to both quantities, the sums will also be equal.
If a = b, then a - c = b - c.
i.e. When two quantities are equal, if you subtract the same number from both quantities, the differences will also be equal.
If a = b, then ac = bc and ca = ba.
i.e. When two quantities are equal, if you multiply them by the same number, the products will also be equal.
If a = b and c does NOT equal 0, then a/c = b/c.
i.e. When two quantities are equal, if they are divided by the same non-zero number, the quotients are also equal.
a = a
i.e. Any number is equal to itself.
If a = b, then b = a.
If a = b and b = c, then a = c.
Bourbaki