The method by which mathematics arrives at its equations is the method of substitution.

For equations express the substitutability of two expressions, and we proceed from a number of equations to new equations, replacing expressions by others in accordance with the equations.

6.241    Thus the proof of the proposition  2 × 2 = 4  runs:

                           (^v)^µ'x=^v×µ'x   Def.
  ^2×2'x = (²)²'x = (²)¹⁺¹'x = ²'²'x = ¹⁺¹'¹⁺¹'x
      = (')'(')'x = ''''x = ^1+1+1+1'x = ⁴'x.