let A be non empty set ; :: thesis: for v being Element of Valuations_in A
for J being interpretation of A holds J,v |= VERUM
let v be Element of Valuations_in A; :: thesis: for J being interpretation of A holds J,v |= VERUM
let J be interpretation of A; :: thesis: J,v |= VERUM
((Valuations_in A) --> TRUE ) . v = TRUE by FUNCOP_1:13;
then (Valid VERUM ,J) . v = TRUE by Lm1;
hence J,v |= VERUM by Def12; :: thesis: verum