%   ORIGINAL: 'h4/thm/bool/MONO_AND_'
% 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: !z y x w. (x ==> y) /\ (z ==> w) ==> x /\ z ==> y /\ w
%   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: !z y x w. (x ==> y) /\ (z ==> w) ==> x /\ z ==> y /\ w
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_3f34578,V_3f34574]: ![F, G]: (![X]: s(V_3f34574,happ(s(fun(V_3f34578,V_3f34574),F),s(V_3f34578,X))) = s(V_3f34574,happ(s(fun(V_3f34578,V_3f34574),G),s(V_3f34578,X))) => s(fun(V_3f34578,V_3f34574),F) = s(fun(V_3f34578,V_3f34574),G))).
fof('h4/thm/bool/MONO_AND_', conjecture, ![Z, Y, X, W]: (((p(s(bool,X)) => p(s(bool,Y))) & (p(s(bool,Z)) => p(s(bool,W)))) => ((p(s(bool,X)) & p(s(bool,Z))) => (p(s(bool,Y)) & p(s(bool,W)))))).
