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Theorem cnveqi 4611
Description: Equality inference for converse. (Contributed by NM, 23-Dec-2008.)
Hypothesis
Ref Expression
cnveqi.1 𝐴 = 𝐵
Assertion
Ref Expression
cnveqi 𝐴 = 𝐵

Proof of Theorem cnveqi
StepHypRef Expression
1 cnveqi.1 . 2 𝐴 = 𝐵
2 cnveq 4610 . 2 (𝐴 = 𝐵𝐴 = 𝐵)
31, 2ax-mp 7 1 𝐴 = 𝐵
Colors of variables: wff set class
Syntax hints:   = wceq 1289  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-17 1464  ax-i9 1468  ax-ial 1472  ax-i5r 1473  ax-ext 2070
This theorem depends on definitions:  df-bi 115  df-nf 1395  df-sb 1693  df-clab 2075  df-cleq 2081  df-clel 2084  df-nfc 2217  df-in 3005  df-ss 3012  df-br 3846  df-opab 3900  df-cnv 4446
This theorem is referenced by:  mptcnv  4834  cnvxp  4850  xp0  4851  imainrect  4876  cnvcnv  4883  mptpreima  4924  co01  4945  coi2  4947  cocnvres  4955  fcoi1  5191  fun11iun  5274  f1ocnvd  5846  cnvoprab  5999  f1od2  6000  mapsncnv  6450  sbthlemi8  6671  caseinj  6778  djuinj  6784  fisumcom2  10828
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