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Theorem elcnvcnvintab 36259
 Description: Two ways of saying a set is an element of the converse of the converse of the intersection of a class. (Contributed by RP, 20-Aug-2020.)
Assertion
Ref Expression
elcnvcnvintab
Distinct variable group:   ,
Allowed substitution hint:   ()

Proof of Theorem elcnvcnvintab
StepHypRef Expression
1 cnvcnv 5295 . . . 4
2 incom 3616 . . . 4
31, 2eqtri 2493 . . 3
43eleq2i 2541 . 2
5 elinintab 36252 . 2
64, 5bitri 257 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wb 189   wa 376  wal 1450   wcel 1904  cab 2457  cvv 3031   cin 3389  cint 4226   cxp 4837  ccnv 4838 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1677  ax-4 1690  ax-5 1766  ax-6 1813  ax-7 1859  ax-9 1913  ax-10 1932  ax-11 1937  ax-12 1950  ax-13 2104  ax-ext 2451  ax-sep 4518  ax-nul 4527  ax-pr 4639 This theorem depends on definitions:  df-bi 190  df-or 377  df-an 378  df-3an 1009  df-tru 1455  df-ex 1672  df-nf 1676  df-sb 1806  df-eu 2323  df-mo 2324  df-clab 2458  df-cleq 2464  df-clel 2467  df-nfc 2601  df-ne 2643  df-ral 2761  df-rex 2762  df-rab 2765  df-v 3033  df-dif 3393  df-un 3395  df-in 3397  df-ss 3404  df-nul 3723  df-if 3873  df-sn 3960  df-pr 3962  df-op 3966  df-int 4227  df-br 4396  df-opab 4455  df-xp 4845  df-rel 4846  df-cnv 4847 This theorem is referenced by:  cnvcnvintabd  36277
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