theorem Th38: :: ALTCAT_4:38

for C being category
for D being non empty subcategory of C
for o1, o2 being Object of C
for p1, p2 being Object of D
for m being Morphism of o1,o2
for m1 being Morphism of o2,o1
for n being Morphism of p1,p2
for n1 being Morphism of p2,p1 st p1 = o1 & p2 = o2 & m = n & m1 = n1 & <^p1,p2^> <> {} & <^p2,p1^> <> {} holds
( ( m is_left_inverse_of m1 implies n is_left_inverse_of n1 ) & ( n is_left_inverse_of n1 implies m is_left_inverse_of m1 ) & ( m is_right_inverse_of m1 implies n is_right_inverse_of n1 ) & ( n is_right_inverse_of n1 implies m is_right_inverse_of m1 ) )