let G be Group; :: thesis: for g1, g2 being Element of G
for H being Subgroup of G st g1 in H & g2 in H holds
g1 * g2 in H
let g1, g2 be Element of G; :: thesis: for H being Subgroup of G st g1 in H & g2 in H holds
g1 * g2 in H
let H be Subgroup of G; :: thesis: ( g1 in H & g2 in H implies g1 * g2 in H )
assume ( g1 in H & g2 in H ) ; :: thesis: g1 * g2 in H
then reconsider h1 = g1, h2 = g2 as Element of H ;
h1 * h2 in H ;
hence g1 * g2 in H by Th43; :: thesis: verum