ensed ▁det achment ▁can ▁prove ▁not ▁only ▁that ▁theorem ▁but ▁also ▁its ▁substitution ▁instance ▁ ▁by ▁using ▁a ▁longer ▁proof . ▁ ▁Note ▁that ▁" D - comple ten ess " ▁is ▁a ▁property ▁of ▁an ▁ax iom atic ▁basis ▁for ▁a ▁system , ▁not ▁an ▁intr insic ▁property ▁of ▁a ▁logic ▁system ▁itself . ▁ ▁J . ▁A . ▁Kal man ▁proved ▁that ▁any ▁conclusion ▁that ▁can ▁be ▁generated ▁by ▁ ▁a ▁sequence ▁of ▁uniform ▁substitution ▁( all ▁instances ▁of ▁a ▁variable ▁are ▁replaced ▁with ▁the ▁same ▁content ) ▁and ▁mod us ▁pon ens ▁steps ▁can ▁either ▁be ▁generated ▁by ▁cond ensed ▁det achment ▁alone , ▁or ▁is ▁a ▁substitution ▁instance ▁of ▁something ▁that ▁can ▁be ▁generated ▁by ▁cond ensed ▁det achment ▁alone . ▁This ▁makes ▁cond ensed ▁det achment ▁useful ▁for ▁any ▁logic ▁system ▁that ▁has ▁mod us ▁pon ens ▁and ▁substitution , ▁regardless ▁of ▁whether ▁or ▁not ▁it ▁is ▁D - complete . ▁ ▁D - notation ▁Since ▁a ▁given ▁major ▁prem ise ▁and ▁a ▁given ▁minor ▁prem ise ▁uniqu ely ▁determine ▁the ▁conclusion ▁( up ▁to ▁variable ▁ren aming ), ▁Mer ed ith ▁observed ▁that ▁it ▁was ▁only ▁necessary ▁to ▁note ▁which ▁two ▁statements ▁were ▁involved ▁and ▁that ▁the ▁cond ensed ▁det achment ▁can ▁be ▁used ▁without ▁any ▁other ▁notation ▁required . ▁This ▁led ▁to ▁the ▁" D - notation " ▁for ▁proofs . ▁ ▁This ▁notation ▁uses ▁the ▁" D " ▁operator ▁to ▁mean ▁cond ensed ▁det achment , ▁and ▁takes ▁ 2 ▁arguments , ▁in ▁a ▁standard