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Mirrors > Home > MPE Home > Th. List > fr0 | Structured version Visualization version Unicode version |
Description: Any relation is well-founded on the empty set. (Contributed by NM, 17-Sep-1993.) |
Ref | Expression |
---|---|
fr0 |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | dffr2 4804 |
. 2
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2 | ss0 3768 |
. . . . 5
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3 | 2 | a1d 25 |
. . . 4
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4 | 3 | necon1ad 2660 |
. . 3
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5 | 4 | imp 436 |
. 2
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6 | 1, 5 | mpgbir 1681 |
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 1677 ax-4 1690 ax-5 1766 ax-6 1813 ax-7 1859 ax-10 1932 ax-11 1937 ax-12 1950 ax-13 2104 ax-ext 2451 |
This theorem depends on definitions: df-bi 190 df-or 377 df-an 378 df-tru 1455 df-ex 1672 df-nf 1676 df-sb 1806 df-clab 2458 df-cleq 2464 df-clel 2467 df-nfc 2601 df-ne 2643 df-ral 2761 df-rex 2762 df-rab 2765 df-v 3033 df-dif 3393 df-in 3397 df-ss 3404 df-nul 3723 df-fr 4798 |
This theorem is referenced by: we0 4834 frsn 4910 frfi 7834 ifr0 36873 |
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