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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 36342 | . 2 ⊢ (𝑅 ∈ Rels → (𝑅 ∈ Rels ↔ Rel 𝑅)) | |
2 | 1 | ibi 270 | 1 ⊢ (𝑅 ∈ Rels → Rel 𝑅) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∈ wcel 2110 Rel wrel 5556 Rels crels 36072 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1803 ax-4 1817 ax-5 1918 ax-6 1976 ax-7 2016 ax-8 2112 ax-9 2120 ax-ext 2708 |
This theorem depends on definitions: df-bi 210 df-an 400 df-tru 1546 df-ex 1788 df-sb 2071 df-clab 2715 df-cleq 2729 df-clel 2816 df-v 3410 df-in 3873 df-ss 3883 df-pw 4515 df-rel 5558 df-rels 36340 |
This theorem is referenced by: elrelscnveq3 36346 elrelscnveq2 36348 dfdisjs5 36560 |
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