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Mirrors > Home > ILE Home > Th. List > sonr | Unicode version |
Description: A strict order relation is irreflexive. (Contributed by NM, 24-Nov-1995.) |
Ref | Expression |
---|---|
sonr |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | sopo 4342 |
. 2
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2 | poirr 4336 |
. 2
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3 | 1, 2 | sylan 283 |
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-ext 2175 |
This theorem depends on definitions: df-bi 117 df-3an 982 df-tru 1367 df-nf 1472 df-sb 1774 df-clab 2180 df-cleq 2186 df-clel 2189 df-nfc 2325 df-ral 2477 df-v 2762 df-un 3157 df-sn 3624 df-pr 3625 df-op 3627 df-br 4030 df-po 4325 df-iso 4326 |
This theorem is referenced by: sotricim 4352 sotritrieq 4354 soirri 5052 addnqprlemfl 7609 addnqprlemfu 7610 mulnqprlemfl 7625 mulnqprlemfu 7626 1ne0sr 7816 |
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