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| Description: "Less than or equal to" is a relation. (Contributed by FL, 2-Aug-2009.) (Revised by Mario Carneiro, 28-Apr-2015.) | 
| Ref | Expression | 
|---|---|
| lerel | ⊢ Rel ≤ | 
| Step | Hyp | Ref | Expression | 
|---|---|---|---|
| 1 | lerelxr 11325 | . 2 ⊢ ≤ ⊆ (ℝ* × ℝ*) | |
| 2 | relxp 5702 | . 2 ⊢ Rel (ℝ* × ℝ*) | |
| 3 | relss 5790 | . 2 ⊢ ( ≤ ⊆ (ℝ* × ℝ*) → (Rel (ℝ* × ℝ*) → Rel ≤ )) | |
| 4 | 1, 2, 3 | mp2 9 | 1 ⊢ Rel ≤ | 
| Colors of variables: wff setvar class | 
| Syntax hints: ⊆ wss 3950 × cxp 5682 Rel wrel 5689 ℝ*cxr 11295 ≤ cle 11297 | 
| This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1794 ax-4 1808 ax-5 1909 ax-6 1966 ax-7 2006 ax-8 2109 ax-9 2117 ax-ext 2707 | 
| This theorem depends on definitions: df-bi 207 df-an 396 df-tru 1542 df-ex 1779 df-sb 2064 df-clab 2714 df-cleq 2728 df-clel 2815 df-v 3481 df-dif 3953 df-ss 3967 df-opab 5205 df-xp 5690 df-rel 5691 df-le 11302 | 
| This theorem is referenced by: dfle2 13190 dflt2 13191 ledm 18636 lern 18637 lefld 18638 letsr 18639 dvle 26047 gtiso 32711 | 
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