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Theorem axun2 4138
Description: A variant of the Axiom of Union ax-un 4136. 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.)
Assertion
Ref Expression
axun2 yz(z yw(z w w x))
Distinct variable group:   x,w,y,z

Proof of Theorem axun2
StepHypRef Expression
1 ax-un 4136 . 2 yz(w(z w w x) → z y)
21bm1.3ii 3869 1 yz(z yw(z w w x))
Colors of variables: wff set class
Syntax hints:   wa 97  wb 98  wal 1240  wex 1378
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-5 1333  ax-7 1334  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-8 1392  ax-4 1397  ax-14 1402  ax-17 1416  ax-i9 1420  ax-ial 1424  ax-sep 3866  ax-un 4136
This theorem depends on definitions:  df-bi 110
This theorem is referenced by: (None)
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