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Theorem cnvex 4881
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 ∈ V
Assertion
Ref Expression
cnvex 𝐴 ∈ V

Proof of Theorem cnvex
StepHypRef Expression
1 cnvex.1 . 2 𝐴 ∈ V
2 cnvexg 4880 . 2 (𝐴 ∈ V → 𝐴 ∈ V)
31, 2ax-mp 7 1 𝐴 ∈ V
Colors of variables: wff set class
Syntax hints:  wcel 1407  Vcvv 2572  ccnv 4369
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 103  ax-ia2 104  ax-ia3 105  ax-io 638  ax-5 1350  ax-7 1351  ax-gen 1352  ax-ie1 1396  ax-ie2 1397  ax-8 1409  ax-10 1410  ax-11 1411  ax-i12 1412  ax-bndl 1413  ax-4 1414  ax-13 1418  ax-14 1419  ax-17 1433  ax-i9 1437  ax-ial 1441  ax-i5r 1442  ax-ext 2036  ax-sep 3900  ax-pow 3952  ax-pr 3969  ax-un 4195
This theorem depends on definitions:  df-bi 114  df-3an 896  df-tru 1260  df-nf 1364  df-sb 1660  df-eu 1917  df-mo 1918  df-clab 2041  df-cleq 2047  df-clel 2050  df-nfc 2181  df-ral 2326  df-rex 2327  df-v 2574  df-un 2947  df-in 2949  df-ss 2956  df-pw 3386  df-sn 3406  df-pr 3407  df-op 3409  df-uni 3606  df-br 3790  df-opab 3844  df-xp 4376  df-rel 4377  df-cnv 4378  df-dm 4380  df-rn 4381
This theorem is referenced by:  funcnvuni  4993  brtpos2  5894  xpcomco  6328  frecfzennn  9332
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