45 Proofs (cont') If there exists a proof of a sentence  from a set  of premises and the standard axiom schemata using Modus Ponens, then  is sa
{"Image DocumentName": "If j is provable from D, then D logically entails j.", "Image ImageDescription": "Proofs (cont\u2019) If there exists a proof of a sentence j from a set D of premises and the standard axiom schemata using Modus Ponens, then j is said to be provable from D, written as. D \u22a2 j. There is a close connection between provability and logical entailment (\u22a7): A set of sentences D logically entails a sentence j. if and only if j is provable from D. Soundness Theorem: If j is provable from D, then D logically entails j. Completeness Theorem: If D logically entails j, then j is provable from D.", "Image XResolution": "37", "Image YResolution": "37", "Image ResolutionUnit": "Pixels/Centimeter", "Image Software": "SlidePlayer", "Image YCbCrPositioning": "Centered"}