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

Theorem cnvex 4856
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 4855 . 2 (𝐴 ∈ V → 𝐴 ∈ V)
31, 2ax-mp 7 1 𝐴 ∈ V
Colors of variables: wff set class
Syntax hints:  wcel 1393  Vcvv 2557  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-13 1404  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  ax-un 4170
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-uni 3581  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:  funcnvuni  4968  brtpos2  5866  xpcomco  6300  frecfzennn  9203
  Copyright terms: Public domain W3C validator