theorem Th24: :: SGRAPH1:24

for X being set
for V being Subset of X
for E being Subset of (TWOELEMENTSETS V)
for v1, v2 being set st v1 in V & v2 in V & v1 <> v2 & SimpleGraphStruct(# V,E #) in SIMPLEGRAPHS X holds
ex v1v2 being finite Subset of (TWOELEMENTSETS V) st
( v1v2 = E \/ {{v1,v2}} & SimpleGraphStruct(# V,v1v2 #) in SIMPLEGRAPHS X )