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8.5.10 Modus probans

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Modus probans says that if the side condition S endorses the conclusion C, written S endorse C, and if the side condition S is known to hold, then we can conclude C. The probans operator A probans S expresses modus probans and was used earlier in Line L04 of the proof of ConditionExample:

PA lemma ConditionExample : #x avoid #h endorse #h imply #a infer #h imply all #x : #a end lemma

prepare proof indentation,proof of ConditionExample : line L00 : Premise >> PA ; line L01 : Condition >> #x avoid #h ; line L02 : Premise >> #h imply #a ; line L03 : Gen ponens L02 >> all #x : ( #h imply #a ) ; line L04 : A5 probans L01 >> all #x : ( #h imply #a ) imply ( #h imply all #x : #a ) ; line L05 : MP ponens L04 ponens L03 >> #h imply all #x : #a qed

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