[John]

There are several methods to find the solution mine is far from the simplest but it is the most explicit.

(x + x') => 1
(1 + x) => 1

(1)
F = y’z’ + x’yz + x’y + xyz + xz’
F = y’z’ +yz(x' + x) + x’y + xz’
F = y’z’ +yz + x’y + xz’

(2)
F = y’z’ +yz + x’y + xz’(y + y')
F = y’z’ +yz + x’y + xyz’ + xy'z’

(3)
F = y’z’ +yz + x’y(z + z') + xyz’ + xy'z’
F = y’z’ +yz + x’yz + x’yz' + xyz’ + xy'z’

(4)
F = y’z’ + yz + x’yz + x’yz' + xyz’ + xy'z’
F = y’z’ + (1 + x')yz + x’yz' + xyz’ + xy'z’
F = y’z’ + yz + x’yz' + xyz’ + xy'z’

(5)
F = y’z’ + yz + x’yz' + xyz’ + xy'z’
F = y’z’ + yz + (x’ + x)yz' + xy'z’
F = y’z’ + yz + yz' + xy'z’

(6)
F = y’z’ + yz + yz' + xy'z’
F = yz + yz' + (1 + x)y'z’
F = yz + yz' + y'z’

(7)
F = yz + yz' + y'z’ + yz'

(8)
F = yz + yz' + y'z’ + yz'
F = y(z + z') + yz' + y'z’
F = y + yz' + y'z’

(9)
F = y + yz' + y'z’
F = y + z'(y + y')
F = y + z'

Q.E.D.