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Mirrors > Home > MPE Home > Th. List > prn0 | Unicode version |
Description: A positive real is not empty. (Contributed by NM, 15-May-1996.) (Revised by Mario Carneiro, 11-May-2013.) (New usage is discouraged.) |
Ref | Expression |
---|---|
prn0 |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | elnpi 8825 |
. . 3
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2 | simpl2 961 |
. . 3
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3 | 1, 2 | sylbi 188 |
. 2
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4 | 0pss 3629 |
. 2
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5 | 3, 4 | sylib 189 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
This theorem is referenced by: 0npr 8829 npomex 8833 genpn0 8840 prlem934 8870 ltaddpr 8871 prlem936 8884 reclem2pr 8885 suplem1pr 8889 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-3 7 ax-mp 8 ax-gen 1552 ax-5 1563 ax-17 1623 ax-9 1662 ax-8 1683 ax-6 1740 ax-7 1745 ax-11 1757 ax-12 1946 ax-ext 2389 |
This theorem depends on definitions: df-bi 178 df-an 361 df-3an 938 df-tru 1325 df-ex 1548 df-nf 1551 df-sb 1656 df-clab 2395 df-cleq 2401 df-clel 2404 df-nfc 2533 df-ne 2573 df-ral 2675 df-rex 2676 df-v 2922 df-dif 3287 df-in 3291 df-ss 3298 df-pss 3300 df-nul 3593 df-np 8818 |
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