Metamath Proof Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > MPE Home > Th. List > lerelxr | Structured version Visualization version Unicode version |
Description: 'Less than or equal' is a relation on extended reals. (Contributed by Mario Carneiro, 28-Apr-2015.) |
Ref | Expression |
---|---|
lerelxr |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-le 10080 | . 2 | |
2 | difss 3737 | . 2 | |
3 | 1, 2 | eqsstri 3635 | 1 |
Colors of variables: wff setvar class |
Syntax hints: cdif 3571 wss 3574 cxp 5112 ccnv 5113 cxr 10073 clt 10074 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-le 10080 |
This theorem is referenced by: lerel 10102 dfle2 11980 dflt2 11981 ledm 17224 lern 17225 letsr 17227 xrsle 19766 znle 19884 |
Copyright terms: Public domain | W3C validator |