If T is a complete theory stronger than ZF${}_{\text{Fin}}$ such that axiom of extensionality for classes + T + $(\exists X){\Phi }_i$ is consistent for 1$\le i\le k$ (each alone), where ${\Phi }_i$ are normal formulae then we show AST + $(\exists X){\Phi }_1+\cdots +(\exists X){\Phi }_k$ + scheme of choice is consistent. As a consequence we get: there is no proper ${\Delta }_1$-formula in AST + scheme of choice. Moreover the complexity of the axioms of AST is studied, e.gẇe show axiom of extensionality is ${\Pi }_1$-formula, but not ${\Sigma }_1$-formula and furthermore prolongation axiom, axioms of choice and cardinalities are ${\Pi }_2$-formulae,...