let C1, C2 be MSCongruence of U1; :: thesis: ( ( for s being SortSymbol of S holds C1 . s = MSCng F,s ) & ( for s being SortSymbol of S holds C2 . s = MSCng F,s ) implies C1 = C2 )
assume that
A16: for s being SortSymbol of S holds C1 . s = MSCng F,s and
A17: for s being SortSymbol of S holds C2 . s = MSCng F,s ; :: thesis: C1 = C2

now

let i be set ; :: thesis: ( i in the carrier of S implies C1 . i = C2 . i )
assume i in the carrier of S ; :: thesis: C1 . i = C2 . i
then reconsider s = i as Element of S ;
( C1 . s = MSCng F,s & C2 . s = MSCng F,s ) by A16, A17;
hence C1 . i = C2 . i ; :: thesis: verum

end;

hence C1 = C2 by PBOOLE:3; :: thesis: verum