![]() |
Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
|
Mirrors > Home > ILE Home > Th. List > 4lt6 | GIF version |
Description: 4 is less than 6. (Contributed by Mario Carneiro, 15-Sep-2013.) |
Ref | Expression |
---|---|
4lt6 | ⊢ 4 < 6 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | 4lt5 9096 | . 2 ⊢ 4 < 5 | |
2 | 5lt6 9100 | . 2 ⊢ 5 < 6 | |
3 | 4re 8998 | . . 3 ⊢ 4 ∈ ℝ | |
4 | 5re 9000 | . . 3 ⊢ 5 ∈ ℝ | |
5 | 6re 9002 | . . 3 ⊢ 6 ∈ ℝ | |
6 | 3, 4, 5 | lttri 8064 | . 2 ⊢ ((4 < 5 ∧ 5 < 6) → 4 < 6) |
7 | 1, 2, 6 | mp2an 426 | 1 ⊢ 4 < 6 |
Colors of variables: wff set class |
Syntax hints: class class class wbr 4005 < clt 7994 4c4 8974 5c5 8975 6c6 8976 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 106 ax-ia2 107 ax-ia3 108 ax-in1 614 ax-in2 615 ax-io 709 ax-5 1447 ax-7 1448 ax-gen 1449 ax-ie1 1493 ax-ie2 1494 ax-8 1504 ax-10 1505 ax-11 1506 ax-i12 1507 ax-bndl 1509 ax-4 1510 ax-17 1526 ax-i9 1530 ax-ial 1534 ax-i5r 1535 ax-13 2150 ax-14 2151 ax-ext 2159 ax-sep 4123 ax-pow 4176 ax-pr 4211 ax-un 4435 ax-setind 4538 ax-cnex 7904 ax-resscn 7905 ax-1cn 7906 ax-1re 7907 ax-icn 7908 ax-addcl 7909 ax-addrcl 7910 ax-mulcl 7911 ax-addcom 7913 ax-addass 7915 ax-i2m1 7918 ax-0lt1 7919 ax-0id 7921 ax-rnegex 7922 ax-pre-lttrn 7927 ax-pre-ltadd 7929 |
This theorem depends on definitions: df-bi 117 df-3an 980 df-tru 1356 df-fal 1359 df-nf 1461 df-sb 1763 df-eu 2029 df-mo 2030 df-clab 2164 df-cleq 2170 df-clel 2173 df-nfc 2308 df-ne 2348 df-nel 2443 df-ral 2460 df-rex 2461 df-rab 2464 df-v 2741 df-dif 3133 df-un 3135 df-in 3137 df-ss 3144 df-pw 3579 df-sn 3600 df-pr 3601 df-op 3603 df-uni 3812 df-br 4006 df-opab 4067 df-xp 4634 df-iota 5180 df-fv 5226 df-ov 5880 df-pnf 7996 df-mnf 7997 df-ltxr 7999 df-2 8980 df-3 8981 df-4 8982 df-5 8983 df-6 8984 |
This theorem is referenced by: 3lt6 9102 pigt3 14350 |
Copyright terms: Public domain | W3C validator |