![]() |
Mathbox for Peter Mazsa |
< Previous
Next >
Nearby theorems |
|
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 36995 | . 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 2107 Rel wrel 5639 Rels crels 36682 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1798 ax-4 1812 ax-5 1914 ax-6 1972 ax-7 2012 ax-8 2109 ax-9 2117 ax-ext 2704 |
This theorem depends on definitions: df-bi 206 df-an 398 df-tru 1545 df-ex 1783 df-sb 2069 df-clab 2711 df-cleq 2725 df-clel 2811 df-v 3446 df-in 3918 df-ss 3928 df-pw 4563 df-rel 5641 df-rels 36993 |
This theorem is referenced by: elrelscnveq3 36999 elrelscnveq2 37001 dfdisjs5 37220 |
Copyright terms: Public domain | W3C validator |