Mathbox for Scott Fenton |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > MPE Home > Th. List > Mathboxes > sssslt1 | Structured version Visualization version Unicode version |
Description: Relationship between surreal set less than and subset. (Contributed by Scott Fenton, 9-Dec-2021.) |
Ref | Expression |
---|---|
sssslt1 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ssltex1 31901 | . . . . 5 | |
2 | 1 | adantr 481 | . . . 4 |
3 | simpr 477 | . . . 4 | |
4 | 2, 3 | ssexd 4805 | . . 3 |
5 | ssltex2 31902 | . . . 4 | |
6 | 5 | adantr 481 | . . 3 |
7 | 4, 6 | jca 554 | . 2 |
8 | ssltss1 31903 | . . . . 5 | |
9 | 8 | adantr 481 | . . . 4 |
10 | 3, 9 | sstrd 3613 | . . 3 |
11 | ssltss2 31904 | . . . 4 | |
12 | 11 | adantr 481 | . . 3 |
13 | ssltsep 31905 | . . . 4 | |
14 | ssralv 3666 | . . . 4 | |
15 | 13, 14 | mpan9 486 | . . 3 |
16 | 10, 12, 15 | 3jca 1242 | . 2 |
17 | brsslt 31900 | . 2 | |
18 | 7, 16, 17 | sylanbrc 698 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wi 4 wa 384 w3a 1037 wcel 1990 wral 2912 cvv 3200 wss 3574 class class class wbr 4653 csur 31793 cslt 31794 csslt 31896 |
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-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-ral 2917 df-rex 2918 df-rab 2921 df-v 3202 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-xp 5120 df-sslt 31897 |
This theorem is referenced by: scutun12 31917 |
Copyright terms: Public domain | W3C validator |