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Theorem cnvxp 4742
 Description: The converse of a cross product. Exercise 11 of [Suppes] p. 67. (Contributed by NM, 14-Aug-1999.) (Proof shortened by Andrew Salmon, 27-Aug-2011.)
Assertion
Ref Expression
cnvxp

Proof of Theorem cnvxp
Dummy variables are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 cnvopab 4726 . . 3
2 ancom 253 . . . 4
32opabbii 3824 . . 3
41, 3eqtri 2060 . 2
5 df-xp 4351 . . 3
65cnveqi 4510 . 2
7 df-xp 4351 . 2
84, 6, 73eqtr4i 2070 1
 Colors of variables: wff set class Syntax hints:   wa 97   wceq 1243   wcel 1393  copab 3817   cxp 4343  ccnv 4344 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-eu 1903  df-mo 1904  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-rel 4352  df-cnv 4353 This theorem is referenced by:  xp0  4743  rnxpm  4752  rnxpss  4754  dminxp  4765  imainrect  4766  tposfo  5886  tposf  5887  xpiderm  6177  xpcomf1o  6299
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