let b be set ; :: thesis: for x being bound_QC-variable
for A being non empty set
for v being Element of Valuations_in A
for a being Element of A st x <> b holds
(v . (x | a)) . b = v . b
let x be bound_QC-variable; :: thesis: for A being non empty set
for v being Element of Valuations_in A
for a being Element of A st x <> b holds
(v . (x | a)) . b = v . b
let A be non empty set ; :: thesis: for v being Element of Valuations_in A
for a being Element of A st x <> b holds
(v . (x | a)) . b = v . b
let v be Element of Valuations_in A; :: thesis: for a being Element of A st x <> b holds
(v . (x | a)) . b = v . b
let a be Element of A; :: thesis: ( x <> b implies (v . (x | a)) . b = v . b )
assume x <> b ; :: thesis: (v . (x | a)) . b = v . b
then not b in dom ({x} --> a) by TARSKI:def 1;
hence (v . (x | a)) . b = v . b by FUNCT_4:11; :: thesis: verum