Mathbox for Scott Fenton |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > MPE Home > Th. List > Mathboxes > elno | Structured version Visualization version Unicode version |
Description: Membership in the surreals. (Shortened proof on 2012-Apr-14, SF). (Contributed by Scott Fenton, 11-Jun-2011.) |
Ref | Expression |
---|---|
elno |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | elex 3212 | . 2 | |
2 | fex 6490 | . . . 4 | |
3 | 2 | ancoms 469 | . . 3 |
4 | 3 | rexlimiva 3028 | . 2 |
5 | feq1 6026 | . . . 4 | |
6 | 5 | rexbidv 3052 | . . 3 |
7 | df-no 31796 | . . 3 | |
8 | 6, 7 | elab2g 3353 | . 2 |
9 | 1, 4, 8 | pm5.21nii 368 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wb 196 wceq 1483 wcel 1990 wrex 2913 cvv 3200 cpr 4179 con0 5723 wf 5884 c1o 7553 c2o 7554 csur 31793 |
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-rep 4771 ax-sep 4781 ax-nul 4789 ax-pr 4906 |
This theorem depends on definitions: df-bi 197 df-or 385 df-an 386 df-3an 1039 df-tru 1486 df-ex 1705 df-nf 1710 df-sb 1881 df-eu 2474 df-mo 2475 df-clab 2609 df-cleq 2615 df-clel 2618 df-nfc 2753 df-ne 2795 df-ral 2917 df-rex 2918 df-reu 2919 df-rab 2921 df-v 3202 df-sbc 3436 df-csb 3534 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-uni 4437 df-iun 4522 df-br 4654 df-opab 4713 df-mpt 4730 df-id 5024 df-xp 5120 df-rel 5121 df-cnv 5122 df-co 5123 df-dm 5124 df-rn 5125 df-res 5126 df-ima 5127 df-iota 5851 df-fun 5890 df-fn 5891 df-f 5892 df-f1 5893 df-fo 5894 df-f1o 5895 df-fv 5896 df-no 31796 |
This theorem is referenced by: nofun 31802 nodmon 31803 norn 31804 elno2 31807 noreson 31813 |
Copyright terms: Public domain | W3C validator |