Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > ILE Home > Th. List > xpcom | Unicode version |
Description: Composition of two cross products. (Contributed by Jim Kingdon, 20-Dec-2018.) |
Ref | Expression |
---|---|
xpcom |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ibar 299 | . . . 4 | |
2 | ancom 264 | . . . . . . . 8 | |
3 | 2 | anbi1i 454 | . . . . . . 7 |
4 | brxp 4629 | . . . . . . . 8 | |
5 | brxp 4629 | . . . . . . . 8 | |
6 | 4, 5 | anbi12i 456 | . . . . . . 7 |
7 | anandi 580 | . . . . . . 7 | |
8 | 3, 6, 7 | 3bitr4i 211 | . . . . . 6 |
9 | 8 | exbii 1592 | . . . . 5 |
10 | 19.41v 1889 | . . . . 5 | |
11 | 9, 10 | bitr2i 184 | . . . 4 |
12 | 1, 11 | bitr2di 196 | . . 3 |
13 | 12 | opabbidv 4042 | . 2 |
14 | df-co 4607 | . 2 | |
15 | df-xp 4604 | . 2 | |
16 | 13, 14, 15 | 3eqtr4g 2222 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wceq 1342 wex 1479 wcel 2135 class class class wbr 3976 copab 4036 cxp 4596 ccom 4602 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-io 699 ax-5 1434 ax-7 1435 ax-gen 1436 ax-ie1 1480 ax-ie2 1481 ax-8 1491 ax-10 1492 ax-11 1493 ax-i12 1494 ax-bndl 1496 ax-4 1497 ax-17 1513 ax-i9 1517 ax-ial 1521 ax-i5r 1522 ax-14 2138 ax-ext 2146 ax-sep 4094 ax-pow 4147 ax-pr 4181 |
This theorem depends on definitions: df-bi 116 df-3an 969 df-tru 1345 df-nf 1448 df-sb 1750 df-clab 2151 df-cleq 2157 df-clel 2160 df-nfc 2295 df-ral 2447 df-rex 2448 df-v 2723 df-un 3115 df-in 3117 df-ss 3124 df-pw 3555 df-sn 3576 df-pr 3577 df-op 3579 df-br 3977 df-opab 4038 df-xp 4604 df-co 4607 |
This theorem is referenced by: (None) |
Copyright terms: Public domain | W3C validator |