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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 35183 | . 2 ⊢ S = {〈𝑥, 𝑦〉 ∣ 𝑥 ⊆ 𝑦} | |
2 | 1 | relopabi 5538 | 1 ⊢ Rel S |
Colors of variables: wff setvar class |
Syntax hints: ⊆ wss 3823 Rel wrel 5406 S cssr 34900 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1758 ax-4 1772 ax-5 1869 ax-6 1928 ax-7 1965 ax-8 2052 ax-9 2059 ax-10 2079 ax-11 2093 ax-12 2106 ax-ext 2744 |
This theorem depends on definitions: df-bi 199 df-an 388 df-or 834 df-3an 1070 df-tru 1510 df-ex 1743 df-nf 1747 df-sb 2016 df-clab 2753 df-cleq 2765 df-clel 2840 df-nfc 2912 df-rab 3091 df-v 3411 df-dif 3826 df-un 3828 df-in 3830 df-ss 3837 df-nul 4173 df-if 4345 df-sn 4436 df-pr 4438 df-op 4442 df-opab 4986 df-xp 5407 df-rel 5408 df-ssr 35183 |
This theorem is referenced by: brssr 35186 issetssr 35188 brcnvssr 35191 extssr 35194 |
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