MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  dfid2 Structured version   Visualization version   GIF version

Theorem dfid2 5428
Description: Alternate definition of the identity relation. (Contributed by NM, 15-Mar-2007.) Use df-id 5425 when sufficient (see comment at dfid3 5427). (New usage is discouraged.)
Assertion
Ref Expression
dfid2 I = {⟨𝑥, 𝑥⟩ ∣ 𝑥 = 𝑥}

Proof of Theorem dfid2
StepHypRef Expression
1 dfid3 5427 1 I = {⟨𝑥, 𝑥⟩ ∣ 𝑥 = 𝑥}
Colors of variables: wff setvar class
Syntax hints:   = wceq 1542  {copab 5089   I cid 5424
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1802  ax-4 1816  ax-5 1916  ax-6 1974  ax-7 2019  ax-8 2115  ax-9 2123  ax-10 2144  ax-11 2161  ax-12 2178  ax-13 2371  ax-ext 2710
This theorem depends on definitions:  df-bi 210  df-an 400  df-or 847  df-3an 1090  df-tru 1545  df-fal 1555  df-ex 1787  df-nf 1791  df-sb 2074  df-clab 2717  df-cleq 2730  df-clel 2811  df-nfc 2881  df-v 3399  df-dif 3844  df-un 3846  df-nul 4210  df-if 4412  df-sn 4514  df-pr 4516  df-op 4520  df-opab 5090  df-id 5425
This theorem is referenced by:  fsplitOLD  7832
  Copyright terms: Public domain W3C validator