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Mirrors > Home > MPE Home > Th. List > po0 | Structured version Visualization version Unicode version |
Description: Any relation is a partial ordering of the empty set. (Contributed by NM, 28-Mar-1997.) (Proof shortened by Andrew Salmon, 25-Jul-2011.) |
Ref | Expression |
---|---|
po0 |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ral0 3873 |
. 2
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2 | df-po 4754 |
. 2
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3 | 1, 2 | mpbir 213 |
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 1668 ax-4 1681 ax-5 1757 ax-6 1804 ax-7 1850 ax-10 1914 ax-11 1919 ax-12 1932 ax-13 2090 ax-ext 2430 |
This theorem depends on definitions: df-bi 189 df-an 373 df-tru 1446 df-ex 1663 df-nf 1667 df-sb 1797 df-clab 2437 df-cleq 2443 df-clel 2446 df-nfc 2580 df-ral 2741 df-v 3046 df-dif 3406 df-nul 3731 df-po 4754 |
This theorem is referenced by: so0 4787 posn 4902 dfpo2 30388 ipo0 36796 |
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