let G be addGroup; :: thesis: for g1, g2 being Element of G
for H being Subgroup of G st g1 in carr H & g2 in carr H holds
g1 + g2 in carr H
let g1, g2 be Element of G; :: thesis: for H being Subgroup of G st g1 in carr H & g2 in carr H holds
g1 + g2 in carr H
let H be Subgroup of G; :: thesis: ( g1 in carr H & g2 in carr H implies g1 + g2 in carr H )
assume ( g1 in carr H & g2 in carr H ) ; :: thesis: g1 + g2 in carr H
then ( g1 in H & g2 in H ) ;
then g1 + g2 in H by Th50;
hence g1 + g2 in carr H ; :: thesis: verum