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Theorem cnveqi 4532
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 4531 . 2 (𝐴 = 𝐵𝐴 = 𝐵)
31, 2ax-mp 7 1 𝐴 = 𝐵
Colors of variables: wff set class
Syntax hints:   = wceq 1285  ccnv 4364
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 663  ax-5 1377  ax-7 1378  ax-gen 1379  ax-ie1 1423  ax-ie2 1424  ax-8 1436  ax-10 1437  ax-11 1438  ax-i12 1439  ax-bndl 1440  ax-4 1441  ax-17 1460  ax-i9 1464  ax-ial 1468  ax-i5r 1469  ax-ext 2064
This theorem depends on definitions:  df-bi 115  df-nf 1391  df-sb 1687  df-clab 2069  df-cleq 2075  df-clel 2078  df-nfc 2209  df-in 2980  df-ss 2987  df-br 3788  df-opab 3842  df-cnv 4373
This theorem is referenced by:  cnvxp  4766  xp0  4767  imainrect  4790  cnvcnv  4797  mptpreima  4838  co01  4859  coi2  4861  fcoi1  5095  fun11iun  5172  f1ocnvd  5727  cnvoprab  5880  f1od2  5881
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