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Theorem dfid2 5456
Description: Alternate definition of the identity relation. (Contributed by NM, 15-Mar-2007.) Use df-id 5453 when sufficient (see comment at dfid3 5455). (New usage is discouraged.)
Assertion
Ref Expression
dfid2 I = {⟨𝑥, 𝑥⟩ ∣ 𝑥 = 𝑥}

Proof of Theorem dfid2
StepHypRef Expression
1 dfid3 5455 1 I = {⟨𝑥, 𝑥⟩ ∣ 𝑥 = 𝑥}
Colors of variables: wff setvar class
Syntax hints:   = wceq 1528  {copab 5119   I cid 5452
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1787  ax-4 1801  ax-5 1902  ax-6 1961  ax-7 2006  ax-8 2107  ax-9 2115  ax-10 2136  ax-11 2151  ax-12 2167  ax-13 2381  ax-ext 2790
This theorem depends on definitions:  df-bi 208  df-an 397  df-or 842  df-3an 1081  df-tru 1531  df-ex 1772  df-nf 1776  df-sb 2061  df-clab 2797  df-cleq 2811  df-clel 2890  df-nfc 2960  df-rab 3144  df-v 3494  df-dif 3936  df-un 3938  df-in 3940  df-ss 3949  df-nul 4289  df-if 4464  df-sn 4558  df-pr 4560  df-op 4564  df-opab 5120  df-id 5453
This theorem is referenced by:  fsplitOLD  7802
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