New Foundations Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  NFE Home  >  Th. List  >  uniiun GIF version

Theorem uniiun 4019
 Description: Class union in terms of indexed union. Definition in [Stoll] p. 43. (Contributed by NM, 28-Jun-1998.)
Assertion
Ref Expression
uniiun A = x A x
Distinct variable group:   x,A

Proof of Theorem uniiun
Dummy variable y is distinct from all other variables.
StepHypRef Expression
1 dfuni2 3893 . 2 A = {y x A y x}
2 df-iun 3971 . 2 x A x = {y x A y x}
31, 2eqtr4i 2376 1 A = x A x
 Colors of variables: wff setvar class Syntax hints:   = wceq 1642   ∈ wcel 1710  {cab 2339  ∃wrex 2615  ∪cuni 3891  ∪ciun 3969 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-7 1734  ax-11 1746  ax-12 1925  ax-ext 2334 This theorem depends on definitions:  df-bi 177  df-an 360  df-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649  df-clab 2340  df-cleq 2346  df-rex 2620  df-uni 3892  df-iun 3971 This theorem is referenced by:  iununi  4050  iunpwss  4055  imauni  5465
 Copyright terms: Public domain W3C validator