ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  dfuni2 Structured version   GIF version

Theorem dfuni2 3573
Description: Alternate definition of class union. (Contributed by NM, 28-Jun-1998.)
Assertion
Ref Expression
dfuni2 A = {xy A x y}
Distinct variable group:   x,y,A

Proof of Theorem dfuni2
StepHypRef Expression
1 df-uni 3572 . 2 A = {xy(x y y A)}
2 exancom 1496 . . . 4 (y(x y y A) ↔ y(y A x y))
3 df-rex 2306 . . . 4 (y A x yy(y A x y))
42, 3bitr4i 176 . . 3 (y(x y y A) ↔ y A x y)
54abbii 2150 . 2 {xy(x y y A)} = {xy A x y}
61, 5eqtri 2057 1 A = {xy A x y}
Colors of variables: wff set class
Syntax hints:   wa 97   = wceq 1242  wex 1378   wcel 1390  {cab 2023  wrex 2301   cuni 3571
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-11 1394  ax-4 1397  ax-17 1416  ax-i9 1420  ax-ial 1424  ax-i5r 1425  ax-ext 2019
This theorem depends on definitions:  df-bi 110  df-tru 1245  df-nf 1347  df-sb 1643  df-clab 2024  df-cleq 2030  df-rex 2306  df-uni 3572
This theorem is referenced by:  nfuni  3577  nfunid  3578  unieq  3580  uniiun  3701
  Copyright terms: Public domain W3C validator