Theorem dfid2 4956

Description: Alternate definition of the identity relation. (Contributed by NM, 15-Mar-2007.)

Assertion

Ref	Expression
dfid2	⊢ I = {⟨𝑥, 𝑥⟩ ∣ 𝑥 = 𝑥}

Proof of Theorem dfid2

Step	Hyp	Ref	Expression
1		dfid3 4954	1 ⊢ I = {⟨𝑥, 𝑥⟩ ∣ 𝑥 = 𝑥}

Syntax hints:   = wceq 1475  {copab 4642   I cid 4948

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1713  ax-4 1728  ax-5 1827  ax-6 1875  ax-7 1922  ax-10 2006  ax-11 2021  ax-12 2034  ax-13 2234  ax-ext 2590

This theorem depends on definitions:  df-bi 196  df-or 384  df-an 385  df-3an 1033  df-tru 1478  df-ex 1696  df-nf 1701  df-sb 1868  df-clab 2597  df-cleq 2603  df-clel 2606  df-nfc 2740  df-rab 2905  df-v 3175  df-dif 3543  df-un 3545  df-in 3547  df-ss 3554  df-nul 3875  df-if 4037  df-sn 4126  df-pr 4128  df-op 4132  df-opab 4644  df-id 4953

This theorem is referenced by:  fsplit  7169