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Mirrors > Home > ILE Home > Th. List > 1lt2o | Unicode version |
Description: Ordinal one is less than ordinal two. (Contributed by Jim Kingdon, 31-Jul-2022.) |
Ref | Expression |
---|---|
1lt2o |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | 1oex 6448 |
. . 3
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2 | 1 | prid2 3714 |
. 2
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3 | df2o3 6454 |
. 2
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4 | 2, 3 | eleqtrri 2265 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() |
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 615 ax-in2 616 ax-io 710 ax-5 1458 ax-7 1459 ax-gen 1460 ax-ie1 1504 ax-ie2 1505 ax-8 1515 ax-10 1516 ax-11 1517 ax-i12 1518 ax-bndl 1520 ax-4 1521 ax-17 1537 ax-i9 1541 ax-ial 1545 ax-i5r 1546 ax-13 2162 ax-14 2163 ax-ext 2171 ax-sep 4136 ax-nul 4144 ax-pow 4192 ax-pr 4227 ax-un 4451 |
This theorem depends on definitions: df-bi 117 df-tru 1367 df-nf 1472 df-sb 1774 df-clab 2176 df-cleq 2182 df-clel 2185 df-nfc 2321 df-ral 2473 df-rex 2474 df-v 2754 df-dif 3146 df-un 3148 df-in 3150 df-ss 3157 df-nul 3438 df-pw 3592 df-sn 3613 df-pr 3614 df-uni 3825 df-tr 4117 df-iord 4384 df-on 4386 df-suc 4389 df-1o 6440 df-2o 6441 |
This theorem is referenced by: infnninf 7151 infnninfOLD 7152 nnnninf 7153 nnnninfeq 7155 nninfisollemne 7158 fodjuf 7172 mkvprop 7185 nninfwlporlemd 7199 nninfwlporlem 7200 nninfwlpoimlemg 7202 nninfwlpoimlemginf 7203 exmidonfinlem 7221 pw1ne3 7258 3nelsucpw1 7262 3nsssucpw1 7264 2oneel 7284 2omotaplemst 7286 unct 12492 xpsfeq 12818 xpsfval 12821 xpsval 12825 bj-charfun 15012 bj-charfundc 15013 012of 15199 pwle2 15202 subctctexmid 15204 nnsf 15208 peano4nninf 15209 nninfsellemcl 15214 nninffeq 15223 |
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