help with the Pior the ice barrier

the oppement use a spell card to summon Prior the ice barrier and then use his effect to summon a level 8 monster, but Prior effect is cannot,but he argue it can by not using the summoning effect
so,is it allow?

Summon condition
"If you control a face-up "Ice Barrier" monster, you can Special Summon this card (from your hand). You cannot Special Summon any Level 5 or higher monsters the turn you use this effect."

is separate.

"You can Tribute this card to target 1 "Ice Barrier" monster in your Graveyard, except "Prior of the Ice Barrier"; Special Summon that target."

so. if you summon prior without using its summon condition, then you can summon a level 5 or higher.

And the best part is you can call PRIORity XD