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Theorem xpcom 4864
 Description: Composition of two cross products. (Contributed by Jim Kingdon, 20-Dec-2018.)
Assertion
Ref Expression
xpcom
Distinct variable groups:   ,   ,   ,

Proof of Theorem xpcom
Dummy variables are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 ibar 285 . . . 4
2 ancom 253 . . . . . . . 8
32anbi1i 431 . . . . . . 7
4 brxp 4375 . . . . . . . 8
5 brxp 4375 . . . . . . . 8
64, 5anbi12i 433 . . . . . . 7
7 anandi 524 . . . . . . 7
83, 6, 73bitr4i 201 . . . . . 6
98exbii 1496 . . . . 5
10 19.41v 1782 . . . . 5
119, 10bitr2i 174 . . . 4
121, 11syl6rbb 186 . . 3
1312opabbidv 3823 . 2
14 df-co 4354 . 2
15 df-xp 4351 . 2
1613, 14, 153eqtr4g 2097 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 97   wceq 1243  wex 1381   wcel 1393   class class class wbr 3764  copab 3817   cxp 4343   ccom 4349 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-io 630  ax-5 1336  ax-7 1337  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-8 1395  ax-10 1396  ax-11 1397  ax-i12 1398  ax-bndl 1399  ax-4 1400  ax-14 1405  ax-17 1419  ax-i9 1423  ax-ial 1427  ax-i5r 1428  ax-ext 2022  ax-sep 3875  ax-pow 3927  ax-pr 3944 This theorem depends on definitions:  df-bi 110  df-3an 887  df-tru 1246  df-nf 1350  df-sb 1646  df-clab 2027  df-cleq 2033  df-clel 2036  df-nfc 2167  df-ral 2311  df-rex 2312  df-v 2559  df-un 2922  df-in 2924  df-ss 2931  df-pw 3361  df-sn 3381  df-pr 3382  df-op 3384  df-br 3765  df-opab 3819  df-xp 4351  df-co 4354 This theorem is referenced by: (None)
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