let p1, p2 be Element of QC-WFF ; :: thesis: for x1, x2, y1, y2 being bound_QC-variable st All x1,y1,p1 = All x2,y2,p2 holds
( x1 = x2 & y1 = y2 & p1 = p2 )
let x1, x2, y1, y2 be bound_QC-variable; :: thesis: ( All x1,y1,p1 = All x2,y2,p2 implies ( x1 = x2 & y1 = y2 & p1 = p2 ) )
assume A1: All x1,y1,p1 = All x2,y2,p2 ; :: thesis: ( x1 = x2 & y1 = y2 & p1 = p2 )
thus x1 = x2 by A1, Th6; :: thesis: ( y1 = y2 & p1 = p2 )
All y1,p1 = All y2,p2 by A1, Th6;
hence ( y1 = y2 & p1 = p2 ) by Th6; :: thesis: verum