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Theorem dfuni2 3893
 Description: Alternate definition of class union. (Contributed by NM, 28-Jun-1998.)
Assertion
Ref Expression
dfuni2 A = {x y A x y}
Distinct variable group:   x,y,A

Proof of Theorem dfuni2
StepHypRef Expression
1 df-uni 3892 . 2 A = {x y(x y y A)}
2 exancom 1586 . . . 4 (y(x y y A) ↔ y(y A x y))
3 df-rex 2620 . . . 4 (y A x yy(y A x y))
42, 3bitr4i 243 . . 3 (y(x y y A) ↔ y A x y)
54abbii 2465 . 2 {x y(x y y A)} = {x y A x y}
61, 5eqtri 2373 1 A = {x y A x y}
 Colors of variables: wff setvar class Syntax hints:   ∧ wa 358  ∃wex 1541   = wceq 1642   ∈ wcel 1710  {cab 2339  ∃wrex 2615  ∪cuni 3891 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 This theorem is referenced by:  nfuni  3897  nfunid  3898  unieq  3900  uniiun  4019
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