I want to know if a job does not have an ‘LI’ CompCode.
SELECT 
    bSLHD.Job, SLCT.SL, APVM.Vendor, APVM.Name, SLCT.CompCode, SLCT.ExpDate 
FROM 
    bSLHD
INNER JOIN 
    SLCT ON bSLHD.SL = SLCT.SL
INNER JOIN 
    APVM ON bSLHD.Vendor = APVM.Vendor
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Answer
It sounds like you want aggregation. Something like this:
SELECT bSLHD.Job
FROM bSLHD INNER JOIN
     SLCT
     ON bSLHD.SL = SLCT.SL INNER JOIN
     APVM
     ON bSLHD.Vendor = APVM.Vendor
GROUP BY bSLHD.Job
HAVING SUM(CASE WHEN SLCT.CompCode = 'LI' THEN 1 ELSE 0 END) = 0;
