# [Wolfram Language (Mathematica)], 62 bytes

    #/.Table[#⋂##&@@#~Select~MemberQ@ii||i->Set@$,{i,Max@#}]&

[Try it online!][TIO-ky7ua0ow]

[Wolfram Language (Mathematica)]: https://www.wolfram.com/wolframscript/
[TIO-ky7ua0ow]: https://tio.run/##y00syUjNTSzJTE78n2b7X1lfLyQxKSc1WvlRd5OyspqDg3JdcGpOanJJnW9qblJqUaBD5vsJ2zNrajJ17YJTSxxUdKozdXwTKxyUa2PV/geWZgLFAooy80qilXXt0hyUY9XqgpMT8@qquaqrDXWMdExqdcC0MZAGkbU6QAljsLCpjhmEC5MH02ApCA2RhFBGOoZGYAlDiEmGYGmwPBYLoIIwIa7a/wA "Wolfram Language (Mathematica) – Try It Online"

The private-use character is [`\[VectorLessEqual]`](https://reference.wolfram.com/language/ref/VectorLessEqual.html).

```
   Table[                                     ,{i,Max@#}]	for positive i up to the max
#/.                                   i->Set@$				remove i if
         #⋂##&@@											  intersection of
                #~Select~MemberQ@i							    lists containing i
                                  i||						  not all <=i
```