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Mirrors > Home > MPE Home > Th. List > Mathboxes > elrelsrelim | Structured version Visualization version GIF version |
Description: The element of the relations class is a relation. (Contributed by Peter Mazsa, 20-Jul-2019.) |
Ref | Expression |
---|---|
elrelsrelim | ⊢ (𝑅 ∈ Rels → Rel 𝑅) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | elrelsrel 38468 | . 2 ⊢ (𝑅 ∈ Rels → (𝑅 ∈ Rels ↔ Rel 𝑅)) | |
2 | 1 | ibi 267 | 1 ⊢ (𝑅 ∈ Rels → Rel 𝑅) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∈ wcel 2105 Rel wrel 5693 Rels crels 38163 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1791 ax-4 1805 ax-5 1907 ax-6 1964 ax-7 2004 ax-8 2107 ax-9 2115 ax-ext 2705 |
This theorem depends on definitions: df-bi 207 df-an 396 df-tru 1539 df-ex 1776 df-sb 2062 df-clab 2712 df-cleq 2726 df-clel 2813 df-ss 3979 df-pw 4606 df-rel 5695 df-rels 38466 |
This theorem is referenced by: elrelscnveq3 38472 elrelscnveq2 38474 dfdisjs5 38693 |
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