let x, y, z be bound_QC-variable; :: thesis: for p, q being Element of QC-WFF
for t, s being bound_QC-variable 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 ; :: thesis: for t, s being bound_QC-variable st Ex x,y,z,p = Ex t,s,q holds
( x = t & y = s & Ex z,p = q )
let t, s be bound_QC-variable; :: 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 Th19; :: thesis: ( y = s & Ex z,p = q )
Ex y,z,p = Ex s,q by A1, Th19;
hence ( y = s & Ex z,p = q ) by Th19; :: thesis: verum