let A be non empty set ; :: thesis: for x being bound_QC-variable
for v being Element of Valuations_in A
for p being Element of Funcs (Valuations_in A),BOOLEAN st (FOR_ALL x,p) . v = TRUE holds
p . v = TRUE
let x be bound_QC-variable; :: thesis: for v being Element of Valuations_in A
for p being Element of Funcs (Valuations_in A),BOOLEAN st (FOR_ALL x,p) . v = TRUE holds
p . v = TRUE
let v be Element of Valuations_in A; :: thesis: for p being Element of Funcs (Valuations_in A),BOOLEAN st (FOR_ALL x,p) . v = TRUE holds
p . v = TRUE
let p be Element of Funcs (Valuations_in A),BOOLEAN ; :: thesis: ( (FOR_ALL x,p) . v = TRUE implies p . v = TRUE )
for y being bound_QC-variable st x <> y holds
v . y = v . y ;
hence ( (FOR_ALL x,p) . v = TRUE implies p . v = TRUE ) by Th8; :: thesis: verum