Theorem axun2

Description: A variant of the Axiom of Union ax-un . For any set x , there exists a set y whose members are exactly the members of the members of x i.e. the union of x . Axiom Union of BellMachover p. 466. (Contributed by NM, 4-Jun-2006)

	Ref	Expression
Assertion	axun2	|- E. y A. z ( z e. y <-> E. w ( z e. w /\ w e. x ) )

Proof

Step	Hyp	Ref	Expression
1		ax-un	|- E. y A. z ( E. w ( z e. w /\ w e. x ) -> z e. y )
2	1	bm1.3ii	|- E. y A. z ( z e. y <-> E. w ( z e. w /\ w e. x ) )