let a, b, c, d be ext-real number ; :: thesis: ( a <= b & c <= d implies min a,c <= min b,d )
A1: ( min a,c <= a & min a,c <= c ) by Th17;
assume ( a <= b & c <= d ) ; :: thesis: min a,c <= min b,d
then ( min a,c <= b & min a,c <= d ) by A1, Th2;
hence min a,c <= min b,d by Def8; :: thesis: verum