Theorem dfid2 5315

Description: Alternate definition of the identity relation. (Contributed by NM, 15-Mar-2007.) Use df-id 5312 when sufficient (see comment at dfid3 5313). (New usage is discouraged.)

Assertion

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

Proof of Theorem dfid2

Step	Hyp	Ref	Expression
1		dfid3 5313	1 ⊢ I = {⟨𝑥, 𝑥⟩ ∣ 𝑥 = 𝑥}

Syntax hints:   = wceq 1507  {copab 4991   I cid 5311

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1758  ax-4 1772  ax-5 1869  ax-6 1928  ax-7 1965  ax-8 2052  ax-9 2059  ax-10 2079  ax-11 2093  ax-12 2106  ax-13 2301  ax-ext 2750

This theorem depends on definitions:  df-bi 199  df-an 388  df-or 834  df-3an 1070  df-tru 1510  df-ex 1743  df-nf 1747  df-sb 2016  df-clab 2759  df-cleq 2771  df-clel 2846  df-nfc 2918  df-rab 3097  df-v 3417  df-dif 3832  df-un 3834  df-in 3836  df-ss 3843  df-nul 4179  df-if 4351  df-sn 4442  df-pr 4444  df-op 4448  df-opab 4992  df-id 5312

This theorem is referenced by:  fsplit  7620