ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  ralunb Unicode version

Theorem ralunb 3118
Description: Restricted quantification over a union. (Contributed by Scott Fenton, 12-Apr-2011.) (Proof shortened by Andrew Salmon, 29-Jun-2011.)
Assertion
Ref Expression
ralunb  u.

Proof of Theorem ralunb
StepHypRef Expression
1 elun 3078 . . . . . 6  u.
21imbi1i 227 . . . . 5  u.
3 jaob 630 . . . . 5
42, 3bitri 173 . . . 4  u.
54albii 1356 . . 3  u.
6 19.26 1367 . . 3
75, 6bitri 173 . 2  u.
8 df-ral 2305 . 2  u.  u.
9 df-ral 2305 . . 3
10 df-ral 2305 . . 3
119, 10anbi12i 433 . 2
127, 8, 113bitr4i 201 1  u.
Colors of variables: wff set class
Syntax hints:   wi 4   wa 97   wb 98   wo 628  wal 1240   wcel 1390  wral 2300    u. cun 2909
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-io 629  ax-5 1333  ax-7 1334  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-8 1392  ax-10 1393  ax-11 1394  ax-i12 1395  ax-bndl 1396  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-clel 2033  df-nfc 2164  df-ral 2305  df-v 2553  df-un 2916
This theorem is referenced by:  ralun  3119  ralprg  3412  raltpg  3414  ralunsn  3559
  Copyright terms: Public domain W3C validator