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Theorem cnvex 4969
Description: The converse of a set is a set. Corollary 6.8(1) of [TakeutiZaring] p. 26. (Contributed by NM, 19-Dec-2003.)
Hypothesis
Ref Expression
cnvex.1  |-  A  e. 
_V
Assertion
Ref Expression
cnvex  |-  `' A  e.  _V

Proof of Theorem cnvex
StepHypRef Expression
1 cnvex.1 . 2  |-  A  e. 
_V
2 cnvexg 4968 . 2  |-  ( A  e.  _V  ->  `' A  e.  _V )
31, 2ax-mp 7 1  |-  `' A  e.  _V
Colors of variables: wff set class
Syntax hints:    e. wcel 1438   _Vcvv 2619   `'ccnv 4437
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-io 665  ax-5 1381  ax-7 1382  ax-gen 1383  ax-ie1 1427  ax-ie2 1428  ax-8 1440  ax-10 1441  ax-11 1442  ax-i12 1443  ax-bndl 1444  ax-4 1445  ax-13 1449  ax-14 1450  ax-17 1464  ax-i9 1468  ax-ial 1472  ax-i5r 1473  ax-ext 2070  ax-sep 3957  ax-pow 4009  ax-pr 4036  ax-un 4260
This theorem depends on definitions:  df-bi 115  df-3an 926  df-tru 1292  df-nf 1395  df-sb 1693  df-eu 1951  df-mo 1952  df-clab 2075  df-cleq 2081  df-clel 2084  df-nfc 2217  df-ral 2364  df-rex 2365  df-v 2621  df-un 3003  df-in 3005  df-ss 3012  df-pw 3431  df-sn 3452  df-pr 3453  df-op 3455  df-uni 3654  df-br 3846  df-opab 3900  df-xp 4444  df-rel 4445  df-cnv 4446  df-dm 4448  df-rn 4449
This theorem is referenced by:  funcnvuni  5083  brtpos2  6016  xpcomco  6542  ssenen  6567  sbthlemi10  6675  exmidfodomrlemim  6827  frecfzennn  9833  hashfacen  10241
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