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Theorem cnveqd 4685
Description: Equality deduction for converse. (Contributed by NM, 6-Dec-2013.)
Hypothesis
Ref Expression
cnveqd.1  |-  ( ph  ->  A  =  B )
Assertion
Ref Expression
cnveqd  |-  ( ph  ->  `' A  =  `' B )

Proof of Theorem cnveqd
StepHypRef Expression
1 cnveqd.1 . 2  |-  ( ph  ->  A  =  B )
2 cnveq 4683 . 2  |-  ( A  =  B  ->  `' A  =  `' B
)
31, 2syl 14 1  |-  ( ph  ->  `' A  =  `' B )
Colors of variables: wff set class
Syntax hints:    -> wi 4    = wceq 1316   `'ccnv 4508
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 683  ax-5 1408  ax-7 1409  ax-gen 1410  ax-ie1 1454  ax-ie2 1455  ax-8 1467  ax-10 1468  ax-11 1469  ax-i12 1470  ax-bndl 1471  ax-4 1472  ax-17 1491  ax-i9 1495  ax-ial 1499  ax-i5r 1500  ax-ext 2099
This theorem depends on definitions:  df-bi 116  df-nf 1422  df-sb 1721  df-clab 2104  df-cleq 2110  df-clel 2113  df-nfc 2247  df-in 3047  df-ss 3054  df-br 3900  df-opab 3960  df-cnv 4517
This theorem is referenced by:  cnvsng  4994  cores2  5021  suppssof1  5967  2ndval2  6022  2nd1st  6046  cnvf1olem  6089  brtpos2  6116  dftpos4  6128  tpostpos  6129  tposf12  6134  xpcomco  6688  infeq123d  6871  fsumcnv  11174  ennnfonelemf1  11858  txswaphmeolem  12416
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