![]() |
Metamath Proof Explorer |
< Previous
Next >
Nearby theorems |
|
Mirrors > Home > MPE Home > Th. List > rele | Structured version Visualization version GIF version |
Description: The membership relation is a relation. (Contributed by NM, 26-Apr-1998.) (Revised by Mario Carneiro, 21-Dec-2013.) |
Ref | Expression |
---|---|
rele | ⊢ Rel E |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-eprel 5580 | . 2 ⊢ E = {⟨𝑥, 𝑦⟩ ∣ 𝑥 ∈ 𝑦} | |
2 | 1 | relopabiv 5820 | 1 ⊢ Rel E |
Colors of variables: wff setvar class |
Syntax hints: E cep 5579 Rel wrel 5681 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1797 ax-4 1811 ax-5 1913 ax-6 1971 ax-7 2011 ax-8 2108 ax-9 2116 ax-ext 2703 |
This theorem depends on definitions: df-bi 206 df-an 397 df-tru 1544 df-ex 1782 df-sb 2068 df-clab 2710 df-cleq 2724 df-clel 2810 df-v 3476 df-in 3955 df-ss 3965 df-opab 5211 df-eprel 5580 df-xp 5682 df-rel 5683 |
This theorem is referenced by: bj-epelg 35944 bj-epelb 35945 cnambfre 36531 brcnvep 37128 |
Copyright terms: Public domain | W3C validator |