| Mathbox for Peter Mazsa |
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| Mirrors > Home > MPE Home > Th. List > Mathboxes > relssr | Structured version Visualization version GIF version | ||
| Description: The subset relation is a relation. (Contributed by Peter Mazsa, 1-Aug-2019.) |
| Ref | Expression |
|---|---|
| relssr | ⊢ Rel S |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | df-ssr 38499 | . 2 ⊢ S = {〈𝑥, 𝑦〉 ∣ 𝑥 ⊆ 𝑦} | |
| 2 | 1 | relopabiv 5830 | 1 ⊢ Rel S |
| Colors of variables: wff setvar class |
| Syntax hints: ⊆ wss 3951 Rel wrel 5690 S cssr 38185 |
| 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-v 3482 df-ss 3968 df-opab 5206 df-xp 5691 df-rel 5692 df-ssr 38499 |
| This theorem is referenced by: brssr 38502 issetssr 38504 brcnvssr 38507 extssr 38510 |
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