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

Theorem riotaeqdv 5731
 Description: Formula-building deduction for iota. (Contributed by NM, 15-Sep-2011.)
Hypothesis
Ref Expression
riotaeqdv.1
Assertion
Ref Expression
riotaeqdv
Distinct variable group:   ,
Allowed substitution hints:   ()   ()   ()

Proof of Theorem riotaeqdv
StepHypRef Expression
1 riotaeqdv.1 . . . . 5
21eleq2d 2209 . . . 4
32anbi1d 460 . . 3
43iotabidv 5109 . 2
5 df-riota 5730 . 2
6 df-riota 5730 . 2
74, 5, 63eqtr4g 2197 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 103   wceq 1331   wcel 1480  cio 5086  crio 5729 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 698  ax-5 1423  ax-7 1424  ax-gen 1425  ax-ie1 1469  ax-ie2 1470  ax-8 1482  ax-10 1483  ax-11 1484  ax-i12 1485  ax-bndl 1486  ax-4 1487  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-i5r 1515  ax-ext 2121 This theorem depends on definitions:  df-bi 116  df-tru 1334  df-nf 1437  df-sb 1736  df-clab 2126  df-cleq 2132  df-clel 2135  df-nfc 2270  df-rex 2422  df-uni 3737  df-iota 5088  df-riota 5730 This theorem is referenced by:  riotaeqbidv  5733
 Copyright terms: Public domain W3C validator