On Sun, 13 Aug 2017, Dave Horsfall wrote:

On Sat, 12 Aug 2017, Steve Johnson wrote:

A little Googling shows that the IF I mentioned was called the 
"arithmetic IF".

Ah yes.  It was in FORTRAN II, as I recall.

It turns out the original FORTRAN (manual published in October 1956; code first shipped around April 1957) included the arithmetic IF as well as the assigned and computed GOTO statements — see chapter 4 of this manual:

J.W. Backus, R.J. Beeber, S. Best, R. Goldberg, H.L. Herrick, R.A. Hughes, L.B. Mitchell, R.A. Nelson, R. Nutt, D. Sayre, P.B. Sheridan, H. Stern, I. Ziller. The FORTRAN Automatic Coding System for the IBM 704 EDPM : Programmer's Reference Manual. Applied Science Division and Programming Research Department, International Business Machines Corporation, October 15, 1956, 51 pages.
http://www.bitsavers.org/pdf/ibm/704/704_FortranProgRefMan_Oct56.pdf

(For more on the original FORTRAN compiler, see http://www.softwarepreservation.org/projects/FORTRAN/.)