%   ORIGINAL: 'h4/thm/bool/EQ_IMP_THM_'
% Assm: HL_TRUTH: T
% Assm: HL_FALSITY: ~F
% Assm: HL_BOOL_CASES: !t. (t <=> T) \/ (t <=> F)
% Assm: HL_EXT: !f g. (!x. f x = g x) ==> f = g
% Goal: !t1 t2. (t1 <=> t2) <=> (t1 ==> t2) /\ (t2 ==> t1)
%   PROCESSED
% Assm ['HL_TRUTH']: T
% Assm ['HL_FALSITY']: ~F
% Assm ['HL_BOOL_CASES']: !t. (t <=> T) \/ (t <=> F)
% Assm ['HL_EXT']: !f g. (!x. happ f x = happ g x) ==> f = g
% Goal: !t1 t2. (t1 <=> t2) <=> (t1 ==> t2) /\ (t2 ==> t1)
fof('HL_TRUTH', axiom, p(s(bool,'T'))).
fof('HL_FALSITY', axiom, ~ (p(s(bool,'F')))).
fof('HL_BOOL_CASES', axiom, ![T]: (s(bool,T) = s(bool,'T') | s(bool,T) = s(bool,'F'))).
fof('HL_EXT', axiom, ![V_3f33928,V_3f33924]: ![F, G]: (![X]: s(V_3f33924,happ(s(fun(V_3f33928,V_3f33924),F),s(V_3f33928,X))) = s(V_3f33924,happ(s(fun(V_3f33928,V_3f33924),G),s(V_3f33928,X))) => s(fun(V_3f33928,V_3f33924),F) = s(fun(V_3f33928,V_3f33924),G))).
fof('h4/thm/bool/EQ_IMP_THM_', conjecture, ![T1, T2]: (s(bool,T1) = s(bool,T2) <=> ((p(s(bool,T1)) => p(s(bool,T2))) & (p(s(bool,T2)) => p(s(bool,T1)))))).
