theorem Th10: :: ISOCAT_2:12

for A, B being Category
for a1, a2 being Object of A
for b1, b2 being Object of B st Hom ([a1,b1],[a2,b2]) <> {} holds
for f being Morphism of A
for g being Morphism of B holds
( [f,g] is Morphism of [a1,b1],[a2,b2] iff ( f is Morphism of a1,a2 & g is Morphism of b1,b2 ) )