Is it valid to use an authentic mawquf hadith and an authentic maqtu' hadith as evidence, and what is the proof for that?

"Mawquf" (suspended narration): This refers to what has been narrated from the Companions, whether a saying or an action. "Maqtu'" (severed narration): This is what is suspended at the level of the Tabi'i (follower of the Companions), whether a saying or an action. It is not an argument (hujjah), but it can be used for corroboration.

As for the "Mawquf," there is disagreement regarding its validity as an argument: 1. It is not an argument. 2. It is not an argument except in matters of worship ('ibadah). 3. It is an argument and is superior to Qiyas (definition) (analogical deduction) (this is the view of Malik, most Hanafis and Hanbalis, and the early view of Al-Shafi'i). 4. It is an argument but is inferior to Qiyas. 5. It is an argument if it became widespread and was not contradicted. 6. It is an argument if it contradicts Qiyas, otherwise not. 7. It is an argument if Qiyas is combined with it. 8. The saying of the two Shaykhs (Abu Bakr and Umar) is an argument, unlike others. 9. The saying of the four Caliphs is an argument, unlike others. 10. The saying of the Caliphs is an argument, except for Ali.

The closest opinion to correctness is that the saying of a Companion, if it becomes widespread and is not contradicted, is an argument and a silent consensus (ijma' sukuti). If it does not become widespread or has an opposing view, then it is not an argument but can be used for corroboration. As for the consensus of the Companions (ijma' as-Sahabah (definition)), it is a definitive argument by agreement.