let a, b, c be ExtReal; :: thesis: ( a in REAL & a <= b & b < c implies b in REAL )
assume that
A1: ( a in REAL & a <= b ) and
A2: b < c ; :: thesis: b in REAL
( b in REAL or b = +infty ) by A1, Th10;
hence b in REAL by A2, Lm9; :: thesis: verum