![]() |
Metamath Proof Explorer |
< Previous
Next >
Nearby theorems |
|
Mirrors > Home > MPE Home > Th. List > dfid2 | Structured version Visualization version GIF version |
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.) |
Ref | Expression |
---|---|
dfid2 | ⊢ I = {〈𝑥, 𝑥〉 ∣ 𝑥 = 𝑥} |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | dfid3 5313 | 1 ⊢ I = {〈𝑥, 𝑥〉 ∣ 𝑥 = 𝑥} |
Colors of variables: wff setvar class |
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 |
Copyright terms: Public domain | W3C validator |