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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 5444 | . 2 ⊢ E = {〈𝑥, 𝑦〉 ∣ 𝑥 ∈ 𝑦} | |
2 | 1 | relopabiv 5674 | 1 ⊢ Rel E |
Colors of variables: wff setvar class |
Syntax hints: E cep 5443 Rel wrel 5540 |
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 1917 ax-6 1975 ax-7 2020 ax-8 2116 ax-9 2124 ax-ext 2711 |
This theorem depends on definitions: df-bi 210 df-an 400 df-tru 1545 df-ex 1787 df-sb 2075 df-clab 2718 df-cleq 2731 df-clel 2812 df-v 3402 df-in 3860 df-ss 3870 df-opab 5103 df-eprel 5444 df-xp 5541 df-rel 5542 |
This theorem is referenced by: bj-epelg 34894 bj-epelb 34895 cnambfre 35481 brcnvep 36060 |
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