Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > ILE Home > Th. List > leadd2dd | Unicode version |
Description: Addition to both sides of 'less than or equal to'. (Contributed by Mario Carneiro, 30-May-2016.) |
Ref | Expression |
---|---|
leidd.1 | |
ltnegd.2 | |
ltadd1d.3 | |
leadd1dd.4 |
Ref | Expression |
---|---|
leadd2dd |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | leadd1dd.4 | . 2 | |
2 | leidd.1 | . . 3 | |
3 | ltnegd.2 | . . 3 | |
4 | ltadd1d.3 | . . 3 | |
5 | 2, 3, 4 | leadd2d 8429 | . 2 |
6 | 1, 5 | mpbid 146 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wcel 2135 class class class wbr 3976 (class class class)co 5836 cr 7743 caddc 7747 cle 7925 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-in1 604 ax-in2 605 ax-io 699 ax-5 1434 ax-7 1435 ax-gen 1436 ax-ie1 1480 ax-ie2 1481 ax-8 1491 ax-10 1492 ax-11 1493 ax-i12 1494 ax-bndl 1496 ax-4 1497 ax-17 1513 ax-i9 1517 ax-ial 1521 ax-i5r 1522 ax-13 2137 ax-14 2138 ax-ext 2146 ax-sep 4094 ax-pow 4147 ax-pr 4181 ax-un 4405 ax-setind 4508 ax-cnex 7835 ax-resscn 7836 ax-1cn 7837 ax-icn 7839 ax-addcl 7840 ax-addrcl 7841 ax-mulcl 7842 ax-addcom 7844 ax-addass 7846 ax-i2m1 7849 ax-0id 7852 ax-rnegex 7853 ax-pre-ltadd 7860 |
This theorem depends on definitions: df-bi 116 df-3an 969 df-tru 1345 df-fal 1348 df-nf 1448 df-sb 1750 df-eu 2016 df-mo 2017 df-clab 2151 df-cleq 2157 df-clel 2160 df-nfc 2295 df-ne 2335 df-nel 2430 df-ral 2447 df-rex 2448 df-rab 2451 df-v 2723 df-dif 3113 df-un 3115 df-in 3117 df-ss 3124 df-pw 3555 df-sn 3576 df-pr 3577 df-op 3579 df-uni 3784 df-br 3977 df-opab 4038 df-xp 4604 df-cnv 4606 df-iota 5147 df-fv 5190 df-ov 5839 df-pnf 7926 df-mnf 7927 df-xr 7928 df-ltxr 7929 df-le 7930 |
This theorem is referenced by: difgtsumgt 9251 exbtwnzlemstep 10173 nn0opthlem2d 10623 cvg1nlemres 10913 resqrexlemcalc3 10944 abstri 11032 maxabsle 11132 bdtrilem 11166 bdtri 11167 trilpolemlt1 13761 |
Copyright terms: Public domain | W3C validator |