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Theorem cnveqi 4538
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 4537 . 2  |-  ( A  =  B  ->  `' A  =  `' B
)
31, 2ax-mp 7 1  |-  `' A  =  `' B
Colors of variables: wff set class
Syntax hints:    = wceq 1285   `'ccnv 4370
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 3794  df-opab 3848  df-cnv 4379
This theorem is referenced by:  cnvxp  4772  xp0  4773  imainrect  4796  cnvcnv  4803  mptpreima  4844  co01  4865  coi2  4867  fcoi1  5101  fun11iun  5178  f1ocnvd  5733  cnvoprab  5886  f1od2  5887
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