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

Theorem ididg 4816
Description: A set is identical to itself. (Contributed by NM, 28-May-2008.) (Proof shortened by Andrew Salmon, 27-Aug-2011.)
Assertion
Ref Expression
ididg (𝐴𝑉𝐴 I 𝐴)

Proof of Theorem ididg
StepHypRef Expression
1 eqid 2193 . 2 𝐴 = 𝐴
2 ideqg 4814 . 2 (𝐴𝑉 → (𝐴 I 𝐴𝐴 = 𝐴))
31, 2mpbiri 168 1 (𝐴𝑉𝐴 I 𝐴)
Colors of variables: wff set class
Syntax hints:  wi 4   = wceq 1364  wcel 2164   class class class wbr 4030   I cid 4320
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-io 710  ax-5 1458  ax-7 1459  ax-gen 1460  ax-ie1 1504  ax-ie2 1505  ax-8 1515  ax-10 1516  ax-11 1517  ax-i12 1518  ax-bndl 1520  ax-4 1521  ax-17 1537  ax-i9 1541  ax-ial 1545  ax-i5r 1546  ax-14 2167  ax-ext 2175  ax-sep 4148  ax-pow 4204  ax-pr 4239
This theorem depends on definitions:  df-bi 117  df-3an 982  df-tru 1367  df-nf 1472  df-sb 1774  df-eu 2045  df-mo 2046  df-clab 2180  df-cleq 2186  df-clel 2189  df-nfc 2325  df-ral 2477  df-rex 2478  df-v 2762  df-un 3158  df-in 3160  df-ss 3167  df-pw 3604  df-sn 3625  df-pr 3626  df-op 3628  df-br 4031  df-opab 4092  df-id 4325  df-xp 4666  df-rel 4667
This theorem is referenced by:  issetid  4817  opelresi  4954  fvi  5615
  Copyright terms: Public domain W3C validator