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

Theorem nfiunya 3676
Description: Bound-variable hypothesis builder for indexed union. (Contributed by Mario Carneiro, 25-Jan-2014.)
Hypotheses
Ref Expression
nfiunya.1  F/_
nfiunya.2  F/_
Assertion
Ref Expression
nfiunya  F/_ U_
Distinct variable group:   ,
Allowed substitution hints:   ()   (,)

Proof of Theorem nfiunya
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 df-iun 3650 . 2  U_  {  |  }
2 nfiunya.1 . . . 4  F/_
3 nfiunya.2 . . . . 5  F/_
43nfcri 2169 . . . 4  F/
52, 4nfrexya 2357 . . 3  F/
65nfab 2179 . 2  F/_ {  |  }
71, 6nfcxfr 2172 1  F/_ U_
Colors of variables: wff set class
Syntax hints:   wcel 1390   {cab 2023   F/_wnfc 2162  wrex 2301   U_ciun 3648
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-rex 2306  df-iun 3650
This theorem is referenced by: (None)
  Copyright terms: Public domain W3C validator