let x be object ; :: thesis: for G being non empty Group-like multMagma
for H being Subgroup of G st x in H holds
x in G
let G be non empty Group-like multMagma ; :: thesis: for H being Subgroup of G st x in H holds
x in G
let H be Subgroup of G; :: thesis: ( x in H implies x in G )
assume x in H ; :: thesis: x in G
then A1: x in the carrier of H ;
the carrier of H c= the carrier of G by Def5;
hence x in G by A1; :: thesis: verum