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Mirrors > Home > MPE Home > Th. List > sotr | Structured version Unicode version |
Description: A strict order relation is a transitive relation. (Contributed by NM, 21-Jan-1996.) |
Ref | Expression |
---|---|
sotr |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | sopo 4759 |
. 2
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2 | potr 4754 |
. 2
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3 | 1, 2 | sylan 471 |
1
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Colors of variables: wff setvar class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1592 ax-4 1603 ax-5 1671 ax-6 1710 ax-7 1730 ax-10 1777 ax-11 1782 ax-12 1794 ax-13 1952 ax-ext 2430 |
This theorem depends on definitions: df-bi 185 df-or 370 df-an 371 df-3an 967 df-tru 1373 df-ex 1588 df-nf 1591 df-sb 1703 df-clab 2437 df-cleq 2443 df-clel 2446 df-nfc 2601 df-ral 2800 df-rab 2804 df-v 3073 df-dif 3432 df-un 3434 df-in 3436 df-ss 3443 df-nul 3739 df-if 3893 df-sn 3979 df-pr 3981 df-op 3985 df-br 4394 df-po 4742 df-so 4743 |
This theorem is referenced by: sotr2 4771 wetrep 4814 wereu2 4818 sotri 5326 sotriOLD 5331 suplub2 7815 slttr 27949 fin2solem 28556 |
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