theorem :: ZF_LANG:42

for x being Variable
for H, H1 being ZF-formula st H is universal holds
( ( x = bound_in H implies ex H1 being ZF-formula st All (x,H1) = H ) & ( ex H1 being ZF-formula st All (x,H1) = H implies x = bound_in H ) & ( H1 = the_scope_of H implies ex x being Variable st All (x,H1) = H ) & ( ex x being Variable st All (x,H1) = H implies H1 = the_scope_of H ) ) by Def33, Def34;