let p, q be Element of HP-WFF ; :: thesis: ( p is pseudo-canonical & p => q is pseudo-canonical implies q is pseudo-canonical )
assume that
A1: p is pseudo-canonical and
A2: p => q is pseudo-canonical ; :: thesis: q is pseudo-canonical
let V be SetValuation; :: according to HILBERT3:def 8 :: thesis: for P being Permutation of V ex x being set st x is_a_fixpoint_of Perm P,q
let P be Permutation of V; :: thesis: ex x being set st x is_a_fixpoint_of Perm P,q
consider x being set such that
A3: x is_a_fixpoint_of Perm P,p by A1, Def8;
consider f being set such that
A4: f is_a_fixpoint_of Perm P,(p => q) by A2, Def8;
dom (Perm P,(p => q)) = SetVal V,(p => q) by FUNCT_2:67
.= Funcs (SetVal V,p),(SetVal V,q) by Def2 ;
then f in Funcs (SetVal V,p),(SetVal V,q) by A4, ABIAN:def 3;
then reconsider f = f as Function of (SetVal V,p),(SetVal V,q) by FUNCT_2:121;
take f . x ; :: thesis: f . x is_a_fixpoint_of Perm P,q
thus f . x is_a_fixpoint_of Perm P,q by A3, A4, Th40; :: thesis: verum