P is Element of ProjCo (GF p) ;
then consider Px, Py, Pz being set such that
A1: ( Px in the carrier of (GF p) & Py in the carrier of (GF p) & Pz in the carrier of (GF p) ) and
A2: P = [Px,Py,Pz] by MCART_1:68;
take Pz ; :: thesis: ( Pz is Element of (GF p) & ( for px, py, pz being set st P = [px,py,pz] holds
Pz = pz ) )
thus ( Pz is Element of (GF p) & ( for px, py, pz being set st P = [px,py,pz] holds
Pz = pz ) ) by A1, A2, XTUPLE_0:3; :: thesis: verum