P is Element of ProjCo (GF p) ;
then consider Px, Py, Pz being object 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 Px ; :: thesis: ( Px is set & Px is Element of (GF p) & ( for px, py, pz being object st P = [px,py,pz] holds
Px = px ) )
thus ( Px is set & Px is Element of (GF p) & ( for px, py, pz being object st P = [px,py,pz] holds
Px = px ) ) by A1, A2, XTUPLE_0:3; :: thesis: verum