stylistic:tone, quality:correction
If-then-else

The 3-ary if-then-else operator known from programming languages can be defined by If = ρ (P 2 2, P 3 4) {\displaystyle {\textit {If}}=\rho (P_{2}^{2},P_{3}^{4})}. Then, for arbitrary x {\displaystyle x},

and

That is, If (x, y, z) {\displaystyle {\textit {If}}(x,y,z)} returns the then-part, y {\displaystyle y}, if the if-part, x {\displaystyle x}, is true, and the else-part, z {\displaystyle z}, otherwise.