Mathbox for Scott Fenton |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > MPE Home > Th. List > Mathboxes > txpss3v | Structured version Visualization version Unicode version |
Description: A tail Cartesian product is a subset of the class of ordered triples. (Contributed by Scott Fenton, 31-Mar-2012.) |
Ref | Expression |
---|---|
txpss3v |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-txp 31961 | . 2 | |
2 | inss1 3833 | . . 3 | |
3 | relco 5633 | . . . 4 | |
4 | vex 3203 | . . . . . . . . 9 | |
5 | vex 3203 | . . . . . . . . 9 | |
6 | 4, 5 | brcnv 5305 | . . . . . . . 8 |
7 | 4 | brres 5402 | . . . . . . . . 9 |
8 | 7 | simprbi 480 | . . . . . . . 8 |
9 | 6, 8 | sylbi 207 | . . . . . . 7 |
10 | 9 | adantl 482 | . . . . . 6 |
11 | 10 | exlimiv 1858 | . . . . 5 |
12 | vex 3203 | . . . . . 6 | |
13 | 12, 5 | opelco 5293 | . . . . 5 |
14 | opelxp 5146 | . . . . . 6 | |
15 | 12, 14 | mpbiran 953 | . . . . 5 |
16 | 11, 13, 15 | 3imtr4i 281 | . . . 4 |
17 | 3, 16 | relssi 5211 | . . 3 |
18 | 2, 17 | sstri 3612 | . 2 |
19 | 1, 18 | eqsstri 3635 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wa 384 wex 1704 wcel 1990 cvv 3200 cin 3573 wss 3574 cop 4183 class class class wbr 4653 cxp 5112 ccnv 5113 cres 5116 ccom 5118 c1st 7166 c2nd 7167 ctxp 31937 |
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-rel 5121 df-cnv 5122 df-co 5123 df-res 5126 df-txp 31961 |
This theorem is referenced by: txprel 31986 brtxp2 31988 pprodss4v 31991 |
Copyright terms: Public domain | W3C validator |