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Theorem cnveqi 4682
 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 4681 . 2 (𝐴 = 𝐵𝐴 = 𝐵)
31, 2ax-mp 5 1 𝐴 = 𝐵
 Colors of variables: wff set class Syntax hints:   = wceq 1314  ◡ccnv 4506 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 681  ax-5 1406  ax-7 1407  ax-gen 1408  ax-ie1 1452  ax-ie2 1453  ax-8 1465  ax-10 1466  ax-11 1467  ax-i12 1468  ax-bndl 1469  ax-4 1470  ax-17 1489  ax-i9 1493  ax-ial 1497  ax-i5r 1498  ax-ext 2097 This theorem depends on definitions:  df-bi 116  df-nf 1420  df-sb 1719  df-clab 2102  df-cleq 2108  df-clel 2111  df-nfc 2245  df-in 3045  df-ss 3052  df-br 3898  df-opab 3958  df-cnv 4515 This theorem is referenced by:  mptcnv  4909  cnvxp  4925  xp0  4926  imainrect  4952  cnvcnv  4959  mptpreima  5000  co01  5021  coi2  5023  cocnvres  5031  fcoi1  5271  fun11iun  5354  f1ocnvd  5938  cnvoprab  6097  f1od2  6098  mapsncnv  6555  sbthlemi8  6818  caseinj  6940  djuinj  6957  fisumcom2  11147
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