let A be QC-alphabet ; :: thesis: for p1, p2 being Element of QC-WFF A
for x1, x2, y1, y2 being bound_QC-variable of A st Ex (x1,y1,p1) = Ex (x2,y2,p2) holds
( x1 = x2 & y1 = y2 & p1 = p2 )
let p1, p2 be Element of QC-WFF A; :: thesis: for x1, x2, y1, y2 being bound_QC-variable of A st Ex (x1,y1,p1) = Ex (x2,y2,p2) holds
( x1 = x2 & y1 = y2 & p1 = p2 )
let x1, x2, y1, y2 be bound_QC-variable of A; :: thesis: ( Ex (x1,y1,p1) = Ex (x2,y2,p2) implies ( x1 = x2 & y1 = y2 & p1 = p2 ) )
assume A1: Ex (x1,y1,p1) = Ex (x2,y2,p2) ; :: thesis: ( x1 = x2 & y1 = y2 & p1 = p2 )
thus x1 = x2 by A1, Th13; :: thesis: ( y1 = y2 & p1 = p2 )
Ex (y1,p1) = Ex (y2,p2) by A1, Th13;
hence ( y1 = y2 & p1 = p2 ) by Th13; :: thesis: verum