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

Theorem nfiunya 3848
 Description: Bound-variable hypothesis builder for indexed union. (Contributed by Mario Carneiro, 25-Jan-2014.)
Hypotheses
Ref Expression
nfiunya.1
nfiunya.2
Assertion
Ref Expression
nfiunya
Distinct variable group:   ,
Allowed substitution hints:   ()   (,)

Proof of Theorem nfiunya
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 df-iun 3822 . 2
2 nfiunya.1 . . . 4
3 nfiunya.2 . . . . 5
43nfcri 2276 . . . 4
52, 4nfrexya 2477 . . 3
65nfab 2287 . 2
71, 6nfcxfr 2279 1
 Colors of variables: wff set class Syntax hints:   wcel 1481  cab 2126  wnfc 2269  wrex 2418  ciun 3820 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 699  ax-5 1424  ax-7 1425  ax-gen 1426  ax-ie1 1470  ax-ie2 1471  ax-8 1483  ax-10 1484  ax-11 1485  ax-i12 1486  ax-bndl 1487  ax-4 1488  ax-17 1507  ax-i9 1511  ax-ial 1515  ax-i5r 1516  ax-ext 2122 This theorem depends on definitions:  df-bi 116  df-tru 1335  df-nf 1438  df-sb 1737  df-clab 2127  df-cleq 2133  df-clel 2136  df-nfc 2271  df-rex 2423  df-iun 3822 This theorem is referenced by: (None)
 Copyright terms: Public domain W3C validator