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Mirrors > Home > MPE Home > Th. List > drsbn0 | Structured version Unicode version |
Description: The base of a directed set is not empty. (Contributed by Stefan O'Rear, 1-Feb-2015.) |
Ref | Expression |
---|---|
drsbn0.b |
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Ref | Expression |
---|---|
drsbn0 |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | drsbn0.b |
. . 3
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2 | eqid 2451 |
. . 3
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3 | 1, 2 | isdrs 15203 |
. 2
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4 | 3 | simp2bi 1004 |
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 ax-nul 4516 |
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-eu 2264 df-clab 2437 df-cleq 2443 df-clel 2446 df-nfc 2599 df-ne 2644 df-ral 2798 df-rex 2799 df-rab 2802 df-v 3067 df-sbc 3282 df-dif 3426 df-un 3428 df-in 3430 df-ss 3437 df-nul 3733 df-if 3887 df-sn 3973 df-pr 3975 df-op 3979 df-uni 4187 df-br 4388 df-iota 5476 df-fv 5521 df-drs 15198 |
This theorem is referenced by: drsdirfi 15207 isipodrs 15430 |
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