Theorem axun2 2864

Description: A variant of the Axiom of Union ax-un 2862. 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.

Assertion

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

Distinct variable group:   x,w,y,z

Proof of Theorem axun2

Step	Hyp	Ref	Expression
1		ax-un 2862	. 2 |- E.yA.z(E.w(z e. w /\ w e. x) -> z e. y)
2	1	bm1.3ii 2702	1 |- E.yA.z(z e. y <-> E.w(z e. w /\ w e. x))

Syntax hints:   <-> wb 146   /\ wa 223  A.wal 953   e. wcel 957  E.wex 979

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-7 961  ax-gen 962  ax-8 963  ax-12 967  ax-14 969  ax-17 970  ax-4 972  ax-5o 974  ax-6o 977  ax-9o 1122  ax-sep 2699  ax-un 2862

This theorem depends on definitions:  df-bi 147  df-or 224  df-an 225  df-ex 980

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