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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 37870 | . 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 2098 Rel wrel 5674 Rels crels 37558 |
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 2697 |
This theorem depends on definitions: df-bi 206 df-an 396 df-tru 1536 df-ex 1774 df-sb 2060 df-clab 2704 df-cleq 2718 df-clel 2804 df-v 3470 df-in 3950 df-ss 3960 df-pw 4599 df-rel 5676 df-rels 37868 |
This theorem is referenced by: elrelscnveq3 37874 elrelscnveq2 37876 dfdisjs5 38095 |
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