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Mirrors > Home > MPE Home > Th. List > lerel | Structured version Visualization version Unicode version |
Description: 'Less or equal to' is a relation. (Contributed by FL, 2-Aug-2009.) (Revised by Mario Carneiro, 28-Apr-2015.) |
Ref | Expression |
---|---|
lerel |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | lerelxr 10101 | . 2 | |
2 | relxp 5227 | . 2 | |
3 | relss 5206 | . 2 | |
4 | 1, 2, 3 | mp2 9 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wss 3574 cxp 5112 wrel 5119 cxr 10073 cle 10075 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1722 ax-4 1737 ax-5 1839 ax-6 1888 ax-7 1935 ax-9 1999 ax-10 2019 ax-11 2034 ax-12 2047 ax-13 2246 ax-ext 2602 |
This theorem depends on definitions: df-bi 197 df-or 385 df-an 386 df-tru 1486 df-ex 1705 df-nf 1710 df-sb 1881 df-clab 2609 df-cleq 2615 df-clel 2618 df-nfc 2753 df-v 3202 df-dif 3577 df-in 3581 df-ss 3588 df-opab 4713 df-xp 5120 df-rel 5121 df-le 10080 |
This theorem is referenced by: dfle2 11980 dflt2 11981 ledm 17224 lern 17225 lefld 17226 letsr 17227 dvle 23770 gtiso 29478 |
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