let x, y, z be ExtReal; ( y = - z implies x * (y + z) = (x * y) + (x * z) )
assume A1:
y = - z
; x * (y + z) = (x * y) + (x * z)
hence x * (y + z) =
x * 0
by Th7
.=
(x * y) - (x * y)
by Th7
.=
(x * y) + (x * (- y))
by Th92
.=
(x * y) + (x * z)
by A1
;
verum