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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 5425 when sufficient (see comment at dfid3 5427). (New usage is discouraged.) |
Ref | Expression |
---|---|
dfid2 | ⊢ I = {〈𝑥, 𝑥〉 ∣ 𝑥 = 𝑥} |
Step | Hyp | Ref | 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 |
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