Intuitionistic Logic Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  ILE Home  >  Th. List  >  rnxpm Unicode version

Theorem rnxpm 4752
 Description: The range of a cross product. Part of Theorem 3.13(x) of [Monk1] p. 37, with non-empty changed to inhabited. (Contributed by Jim Kingdon, 12-Dec-2018.)
Assertion
Ref Expression
rnxpm
Distinct variable group:   ,
Allowed substitution hint:   ()

Proof of Theorem rnxpm
StepHypRef Expression
1 df-rn 4356 . . 3
2 cnvxp 4742 . . . 4
32dmeqi 4536 . . 3
41, 3eqtri 2060 . 2
5 dmxpm 4555 . 2
64, 5syl5eq 2084 1
 Colors of variables: wff set class Syntax hints:   wi 4   wceq 1243  wex 1381   wcel 1393   cxp 4343  ccnv 4344   cdm 4345   crn 4346 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  df-dm 4355  df-rn 4356 This theorem is referenced by:  ssxpbm  4756  ssxp2  4758  xpexr2m  4762  xpima2m  4768  unixpm  4853
 Copyright terms: Public domain W3C validator