theorem :: LATSUBGR:9

for G1, G2 being Group
for f being Homomorphism of G1,G2
for H1, H2 being Subgroup of G2
for H3, H4 being Subgroup of G1 st the carrier of H3 = f " the carrier of H1 & the carrier of H4 = f " the carrier of H2 & H1 is Subgroup of H2 holds
H3 is Subgroup of H4