let A be QC-alphabet ; :: thesis: for x, y, z being bound_QC-variable of A
for p, q being Element of QC-WFF A
for s, t being bound_QC-variable of A st Ex (x,y,z,p) = Ex (t,s,q) holds
( x = t & y = s & Ex (z,p) = q )
let x, y, z be bound_QC-variable of A; :: thesis: for p, q being Element of QC-WFF A
for s, t being bound_QC-variable of A st Ex (x,y,z,p) = Ex (t,s,q) holds
( x = t & y = s & Ex (z,p) = q )
let p, q be Element of QC-WFF A; :: thesis: for s, t being bound_QC-variable of A st Ex (x,y,z,p) = Ex (t,s,q) holds
( x = t & y = s & Ex (z,p) = q )
let s, t be bound_QC-variable of A; :: thesis: ( Ex (x,y,z,p) = Ex (t,s,q) implies ( x = t & y = s & Ex (z,p) = q ) )
assume A1: Ex (x,y,z,p) = Ex (t,s,q) ; :: thesis: ( x = t & y = s & Ex (z,p) = q )
hence x = t by Th13; :: thesis: ( y = s & Ex (z,p) = q )
Ex (y,z,p) = Ex (s,q) by A1, Th13;
hence ( y = s & Ex (z,p) = q ) by Th13; :: thesis: verum