let R be Ring; :: thesis: for V being RightMod of R
for W1, W2 being Submodule of V
for x being object holds
( x in W1 /\ W2 iff ( x in W1 & x in W2 ) )
let V be RightMod of R; :: thesis: for W1, W2 being Submodule of V
for x being object holds
( x in W1 /\ W2 iff ( x in W1 & x in W2 ) )
let W1, W2 be Submodule of V; :: thesis: for x being object holds
( x in W1 /\ W2 iff ( x in W1 & x in W2 ) )
let x be object ; :: thesis: ( x in W1 /\ W2 iff ( x in W1 & x in W2 ) )
( x in W1 /\ W2 iff x in the carrier of W1 /\ the carrier of W2 ) by Def2;
then ( x in W1 /\ W2 iff ( x in the carrier of W1 & x in the carrier of W2 ) ) by XBOOLE_0:def 4;
hence ( x in W1 /\ W2 iff ( x in W1 & x in W2 ) ) ; :: thesis: verum