Substitution property of equality

In mathematics, the substitution property of equality states:

• For any quantities a and b and any expression F(x), if a = b, then F(a) = F(b) (if either side makes sense).

In first order logic, this is a schema, since we can't quantify over expressions like F (which would be a functional predicate).

Some specific examples of this are:

• For any real numbers a, b, and c, if a = b, then a + c = b + c (here F(x) is x + c);
• For any real numbers a, b, and c, if a = b, then a - c = b - c (here F(x) is x - c);
• For any real numbers a, b, and c, if a = b, then ac = bc (here F(x) is xc);
• For any real numbers a, b, and c, if a = b and c is not zero, then /c/c (here F(x) is /c

See also: reflexive property of equality, symmetric property of equality, transitive property of equality