let Al be QC-alphabet ; :: thesis: for A being non empty set
for x being bound_QC-variable of Al
for v being Element of Valuations_in (Al,A)
for p being Element of Funcs ((Valuations_in (Al,A)),BOOLEAN) st (FOR_ALL (x,p)) . v = TRUE holds
p . v = TRUE
let A be non empty set ; :: thesis: for x being bound_QC-variable of Al
for v being Element of Valuations_in (Al,A)
for p being Element of Funcs ((Valuations_in (Al,A)),BOOLEAN) st (FOR_ALL (x,p)) . v = TRUE holds
p . v = TRUE
let x be bound_QC-variable of Al; :: thesis: for v being Element of Valuations_in (Al,A)
for p being Element of Funcs ((Valuations_in (Al,A)),BOOLEAN) st (FOR_ALL (x,p)) . v = TRUE holds
p . v = TRUE
let v be Element of Valuations_in (Al,A); :: thesis: for p being Element of Funcs ((Valuations_in (Al,A)),BOOLEAN) st (FOR_ALL (x,p)) . v = TRUE holds
p . v = TRUE
let p be Element of Funcs ((Valuations_in (Al,A)),BOOLEAN); :: thesis: ( (FOR_ALL (x,p)) . v = TRUE implies p . v = TRUE )
for y being bound_QC-variable of Al st x <> y holds
v . y = v . y ;
hence ( (FOR_ALL (x,p)) . v = TRUE implies p . v = TRUE ) by Th3; :: thesis: verum