Let us not be desirous of vain glory, provoking one another, envying one another.
'Let us not BECOME' х ginometha (G1096)]. While not asserting that the Galatians are "vain-glorious" now, he says they are liable to become so.
Provoking, [ prokaloumenoi (G4292 ): challenging] one another - an effect of 'vain-gloriousness' on the stronger, as "envying" on the weaker. A danger common both to the orthodox and Judaizing Galatians.