![]() |
Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
|
Mirrors > Home > ILE Home > Th. List > 0lt2o | Unicode version |
Description: Ordinal zero is less than ordinal two. (Contributed by Jim Kingdon, 31-Jul-2022.) |
Ref | Expression |
---|---|
0lt2o |
![]() ![]() ![]() ![]() |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | 0ex 3995 |
. . 3
![]() ![]() ![]() ![]() | |
2 | 1 | prid1 3576 |
. 2
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
3 | df2o3 6257 |
. 2
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
4 | 2, 3 | eleqtrri 2175 |
1
![]() ![]() ![]() ![]() |
Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-in1 584 ax-in2 585 ax-io 671 ax-5 1391 ax-7 1392 ax-gen 1393 ax-ie1 1437 ax-ie2 1438 ax-8 1450 ax-10 1451 ax-11 1452 ax-i12 1453 ax-bndl 1454 ax-4 1455 ax-17 1474 ax-i9 1478 ax-ial 1482 ax-i5r 1483 ax-ext 2082 ax-nul 3994 |
This theorem depends on definitions: df-bi 116 df-tru 1302 df-nf 1405 df-sb 1704 df-clab 2087 df-cleq 2093 df-clel 2096 df-nfc 2229 df-v 2643 df-dif 3023 df-un 3025 df-nul 3311 df-sn 3480 df-pr 3481 df-suc 4231 df-1o 6243 df-2o 6244 |
This theorem is referenced by: fodjuf 6929 mkvprop 6943 pwle2 12779 0nninf 12781 nninfalllemn 12786 nninfsellemcl 12791 nninffeq 12800 isomninnlem 12809 |
Copyright terms: Public domain | W3C validator |