| Mathbox for Peter Mazsa |
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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 38488 | . 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 2108 Rel wrel 5690 Rels crels 38184 |
| This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1795 ax-4 1809 ax-5 1910 ax-6 1967 ax-7 2007 ax-8 2110 ax-9 2118 ax-ext 2708 |
| This theorem depends on definitions: df-bi 207 df-an 396 df-tru 1543 df-ex 1780 df-sb 2065 df-clab 2715 df-cleq 2729 df-clel 2816 df-ss 3968 df-pw 4602 df-rel 5692 df-rels 38486 |
| This theorem is referenced by: elrelscnveq3 38492 elrelscnveq2 38494 dfdisjs5 38713 |
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