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Mirrors > Home > MPE Home > Th. List > el1o | Structured version Visualization version Unicode version |
Description: Membership in ordinal one. (Contributed by NM, 5-Jan-2005.) |
Ref | Expression |
---|---|
el1o |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df1o2 7572 | . . 3 | |
2 | 1 | eleq2i 2693 | . 2 |
3 | 0ex 4790 | . . 3 | |
4 | 3 | elsn2 4211 | . 2 |
5 | 2, 4 | bitri 264 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wb 196 wceq 1483 wcel 1990 c0 3915 csn 4177 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-nul 4789 |
This theorem depends on definitions: df-bi 197 df-or 385 df-an 386 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-v 3202 df-dif 3577 df-un 3579 df-nul 3916 df-sn 4178 df-suc 5729 df-1o 7560 |
This theorem is referenced by: 0lt1o 7584 oelim2 7675 oeeulem 7681 oaabs2 7725 map0e 7895 map1 8036 cantnff 8571 cnfcom3lem 8600 cfsuc 9079 pf1ind 19719 mavmul0 20358 cramer0 20496 |
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