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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 5571 | . 2 ⊢ E = {⟨𝑥, 𝑦⟩ ∣ 𝑥 ∈ 𝑦} | |
2 | 1 | relopabiv 5811 | 1 ⊢ Rel E |
Colors of variables: wff setvar class |
Syntax hints: E cep 5570 Rel wrel 5672 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1789 ax-4 1803 ax-5 1905 ax-6 1963 ax-7 2003 ax-8 2100 ax-9 2108 ax-ext 2695 |
This theorem depends on definitions: df-bi 206 df-an 396 df-tru 1536 df-ex 1774 df-sb 2060 df-clab 2702 df-cleq 2716 df-clel 2802 df-v 3468 df-in 3948 df-ss 3958 df-opab 5202 df-eprel 5571 df-xp 5673 df-rel 5674 |
This theorem is referenced by: bj-epelg 36440 bj-epelb 36441 cnambfre 37030 brcnvep 37627 |
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