P is Element of ProjCo (GF p) ;
then consider Px, Py, Pz being object such that
A6: ( Px in the carrier of (GF p) & Py in the carrier of (GF p) & Pz in the carrier of (GF p) ) and
A7: P = [Px,Py,Pz] by MCART_1:68;
take Py ; :: thesis: ( Py is set & Py is Element of (GF p) & ( for px, py, pz being object st P = [px,py,pz] holds
Py = py ) )
thus ( Py is set & Py is Element of (GF p) & ( for px, py, pz being object st P = [px,py,pz] holds
Py = py ) ) by A6, A7, XTUPLE_0:3; :: thesis: verum