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Mirrors > Home > ILE Home > Th. List > addgt0ii | Unicode version |
Description: Addition of 2 positive numbers is positive. (Contributed by NM, 18-May-1999.) |
Ref | Expression |
---|---|
lt2.1 | |
lt2.2 | |
addgt0i.3 | |
addgt0i.4 |
Ref | Expression |
---|---|
addgt0ii |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | addgt0i.3 | . 2 | |
2 | addgt0i.4 | . 2 | |
3 | lt2.1 | . . 3 | |
4 | lt2.2 | . . 3 | |
5 | 3, 4 | addgt0i 8382 | . 2 |
6 | 1, 2, 5 | mp2an 423 | 1 |
Colors of variables: wff set class |
Syntax hints: wcel 2136 class class class wbr 3981 (class class class)co 5841 cr 7748 cc0 7749 caddc 7752 clt 7929 |
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 1435 ax-7 1436 ax-gen 1437 ax-ie1 1481 ax-ie2 1482 ax-8 1492 ax-10 1493 ax-11 1494 ax-i12 1495 ax-bndl 1497 ax-4 1498 ax-17 1514 ax-i9 1518 ax-ial 1522 ax-i5r 1523 ax-13 2138 ax-14 2139 ax-ext 2147 ax-sep 4099 ax-pow 4152 ax-pr 4186 ax-un 4410 ax-setind 4513 ax-cnex 7840 ax-resscn 7841 ax-1cn 7842 ax-1re 7843 ax-icn 7844 ax-addcl 7845 ax-addrcl 7846 ax-mulcl 7847 ax-addcom 7849 ax-addass 7851 ax-i2m1 7854 ax-0id 7857 ax-rnegex 7858 ax-pre-lttrn 7863 ax-pre-ltadd 7865 |
This theorem depends on definitions: df-bi 116 df-3an 970 df-tru 1346 df-fal 1349 df-nf 1449 df-sb 1751 df-eu 2017 df-mo 2018 df-clab 2152 df-cleq 2158 df-clel 2161 df-nfc 2296 df-ne 2336 df-nel 2431 df-ral 2448 df-rex 2449 df-rab 2452 df-v 2727 df-dif 3117 df-un 3119 df-in 3121 df-ss 3128 df-pw 3560 df-sn 3581 df-pr 3582 df-op 3584 df-uni 3789 df-br 3982 df-opab 4043 df-xp 4609 df-iota 5152 df-fv 5195 df-ov 5844 df-pnf 7931 df-mnf 7932 df-ltxr 7934 |
This theorem is referenced by: eqneg 8624 2pos 8944 3pos 8947 4pos 8950 5pos 8953 6pos 8954 7pos 8955 8pos 8956 9pos 8957 |
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