New Foundations Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  NFE Home  >  Th. List  >  dfuni12 Unicode version

Theorem dfuni12 4291
 Description: Alternate definition of unit union. (Contributed by SF, 15-Mar-2015.)
Assertion
Ref Expression
dfuni12 1 P6 k

Proof of Theorem dfuni12
Dummy variables are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 19.27v 1894 . . . 4
2 vex 2862 . . . . . 6
3 snex 4111 . . . . . 6
42, 3opkelxpk 4248 . . . . 5 k
54albii 1566 . . . 4 k
62ax-gen 1546 . . . . 5
76biantrur 492 . . . 4
81, 5, 73bitr4ri 269 . . 3 k
9 vex 2862 . . . 4
109eluni1 4173 . . 3 1
11 elp6 4263 . . . 4 P6 k k
129, 11ax-mp 5 . . 3 P6 k k
138, 10, 123bitr4i 268 . 2 1 P6 k
1413eqriv 2350 1 1 P6 k
 Colors of variables: wff setvar class Syntax hints:   wb 176   wa 358  wal 1540   wceq 1642   wcel 1710  cvv 2859  csn 3737  copk 4057  ⋃1cuni1 4133   k cxpk 4174   P6 cp6 4178 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 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  ax-nin 4078  ax-sn 4087 This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-3an 936  df-nan 1288  df-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649  df-clab 2340  df-cleq 2346  df-clel 2349  df-nfc 2478  df-ne 2518  df-ral 2619  df-rex 2620  df-v 2861  df-nin 3211  df-compl 3212  df-in 3213  df-un 3214  df-dif 3215  df-ss 3259  df-nul 3551  df-sn 3741  df-pr 3742  df-uni 3892  df-opk 4058  df-1c 4136  df-uni1 4138  df-xpk 4185  df-p6 4191 This theorem is referenced by:  uni1exg  4292
 Copyright terms: Public domain W3C validator