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Theorem cnveqi 4778
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 4777 . 2 (𝐴 = 𝐵𝐴 = 𝐵)
31, 2ax-mp 5 1 𝐴 = 𝐵
Colors of variables: wff set class
Syntax hints:   = wceq 1343  ccnv 4602
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 699  ax-5 1435  ax-7 1436  ax-gen 1437  ax-ie1 1481  ax-ie2 1482  ax-8 1492  ax-10 1493  ax-11 1494  ax-i12 1495  ax-bndl 1497  ax-4 1498  ax-17 1514  ax-i9 1518  ax-ial 1522  ax-i5r 1523  ax-ext 2147
This theorem depends on definitions:  df-bi 116  df-nf 1449  df-sb 1751  df-clab 2152  df-cleq 2158  df-clel 2161  df-nfc 2296  df-in 3121  df-ss 3128  df-br 3982  df-opab 4043  df-cnv 4611
This theorem is referenced by:  mptcnv  5005  cnvxp  5021  xp0  5022  imainrect  5048  cnvcnv  5055  mptpreima  5096  co01  5117  coi2  5119  cocnvres  5127  fcoi1  5367  fun11iun  5452  f1ocnvd  6039  cnvoprab  6198  f1od2  6199  mapsncnv  6657  sbthlemi8  6925  caseinj  7050  djuinj  7067  fisumcom2  11375  fprodcom2fi  11563
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