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Theorem cnveqd 4580
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 4578 . 2  |-  ( A  =  B  ->  `' A  =  `' B
)
31, 2syl 14 1  |-  ( ph  ->  `' A  =  `' B )
Colors of variables: wff set class
Syntax hints:    -> wi 4    = wceq 1287   `'ccnv 4410
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 1379  ax-7 1380  ax-gen 1381  ax-ie1 1425  ax-ie2 1426  ax-8 1438  ax-10 1439  ax-11 1440  ax-i12 1441  ax-bndl 1442  ax-4 1443  ax-17 1462  ax-i9 1466  ax-ial 1470  ax-i5r 1471  ax-ext 2067
This theorem depends on definitions:  df-bi 115  df-nf 1393  df-sb 1690  df-clab 2072  df-cleq 2078  df-clel 2081  df-nfc 2214  df-in 2994  df-ss 3001  df-br 3821  df-opab 3875  df-cnv 4419
This theorem is referenced by:  cnvsng  4882  cores2  4909  suppssof1  5829  2ndval2  5884  2nd1st  5907  cnvf1olem  5946  brtpos2  5970  dftpos4  5982  tpostpos  5983  tposf12  5988  xpcomco  6494  infeq123d  6655
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