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Theorem cnveqi 4510
 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 4509 . 2 (𝐴 = 𝐵𝐴 = 𝐵)
31, 2ax-mp 7 1 𝐴 = 𝐵
 Colors of variables: wff set class Syntax hints:   = wceq 1243  ◡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-17 1419  ax-i9 1423  ax-ial 1427  ax-i5r 1428  ax-ext 2022 This theorem depends on definitions:  df-bi 110  df-nf 1350  df-sb 1646  df-clab 2027  df-cleq 2033  df-clel 2036  df-nfc 2167  df-in 2924  df-ss 2931  df-br 3765  df-opab 3819  df-cnv 4353 This theorem is referenced by:  cnvxp  4742  xp0  4743  imainrect  4766  cnvcnv  4773  mptpreima  4814  co01  4835  coi2  4837  fcoi1  5070  fun11iun  5147  f1ocnvd  5702
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