reserve A for QC-alphabet;
reserve X,T for Subset of CQC-WFF(A);
reserve F,G,H,p,q,r,t for Element of CQC-WFF(A);
reserve s,h for QC-formula of A;
reserve x,y for bound_QC-variable of A;
reserve f for FinSequence of [:CQC-WFF(A),Proof_Step_Kinds:];
reserve i,j for Element of NAT;

theorem Th12:
  (s => h).x = (s.x) => (h.x)
proof
  s => h = 'not'(s '&' 'not' h) by QC_LANG2:def 2;
  hence (s => h).x = 'not'((s '&' 'not' h).x) by CQC_LANG:19
    .= 'not'((s.x) '&' ('not' h).x) by CQC_LANG:21
    .= 'not'((s.x) '&' 'not'(h.x)) by CQC_LANG:19
    .= (s.x) => (h.x) by QC_LANG2:def 2;
end;
