18a omission of prep?

τί δὲ τροφήν; ἆρ᾽ οὐ γυμναστικῇ καὶ μουσικῇ μαθήμασίν τε ὅσα προσήκει τούτοις, ἐν ἅπασι τεθράφθαι;
Is the prep εν omitted before γυμναστικῇ καὶ μουσικῇ or is it instrumental Dative?
The commentary says Stalbaum had difficulty with the preposition and decided to delete it, making everything instrumental.