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Mirrors > Home > MPE Home > Th. List > 0we1 | Structured version Visualization version Unicode version |
Description: The empty set is a well-ordering of ordinal one. (Contributed by Mario Carneiro, 9-Feb-2015.) |
Ref | Expression |
---|---|
0we1 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | br0 4701 | . . 3 | |
2 | rel0 5243 | . . . 4 | |
3 | wesn 5190 | . . . 4 | |
4 | 2, 3 | ax-mp 5 | . . 3 |
5 | 1, 4 | mpbir 221 | . 2 |
6 | df1o2 7572 | . . 3 | |
7 | weeq2 5103 | . . 3 | |
8 | 6, 7 | ax-mp 5 | . 2 |
9 | 5, 8 | mpbir 221 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wn 3 wb 196 wceq 1483 c0 3915 csn 4177 class class class wbr 4653 wwe 5072 wrel 5119 c1o 7553 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1722 ax-4 1737 ax-5 1839 ax-6 1888 ax-7 1935 ax-9 1999 ax-10 2019 ax-11 2034 ax-12 2047 ax-13 2246 ax-ext 2602 ax-sep 4781 ax-nul 4789 ax-pr 4906 |
This theorem depends on definitions: df-bi 197 df-or 385 df-an 386 df-3or 1038 df-3an 1039 df-tru 1486 df-ex 1705 df-nf 1710 df-sb 1881 df-clab 2609 df-cleq 2615 df-clel 2618 df-nfc 2753 df-ne 2795 df-ral 2917 df-rex 2918 df-rab 2921 df-v 3202 df-sbc 3436 df-dif 3577 df-un 3579 df-in 3581 df-ss 3588 df-nul 3916 df-if 4087 df-sn 4178 df-pr 4180 df-op 4184 df-br 4654 df-opab 4713 df-po 5035 df-so 5036 df-fr 5073 df-we 5075 df-xp 5120 df-rel 5121 df-suc 5729 df-1o 7560 |
This theorem is referenced by: psr1tos 19559 |
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