theorem Th6: :: TOPREAL5:6

for ra, rb, a, b being Real st ra < rb holds
for f being continuous Function of (Closed-Interval-TSpace (ra,rb)),R^1
for d being Real st f . ra = a & f . rb = b & a < d & d < b holds
ex rc being Real st
( f . rc = d & ra < rc & rc < rb )