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Theorem cnveqd 4454
 Description: Equality deduction for converse. (Contributed by NM, 6-Dec-2013.)
Hypothesis
Ref Expression
cnveqd.1 (φA = B)
Assertion
Ref Expression
cnveqd (φA = B)

Proof of Theorem cnveqd
StepHypRef Expression
1 cnveqd.1 . 2 (φA = B)
2 cnveq 4452 . 2 (A = BA = B)
31, 2syl 14 1 (φA = B)
 Colors of variables: wff set class Syntax hints:   → wi 4   = wceq 1242  ◡ccnv 4287 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 629  ax-5 1333  ax-7 1334  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-8 1392  ax-10 1393  ax-11 1394  ax-i12 1395  ax-bnd 1396  ax-4 1397  ax-17 1416  ax-i9 1420  ax-ial 1424  ax-i5r 1425  ax-ext 2019 This theorem depends on definitions:  df-bi 110  df-nf 1347  df-sb 1643  df-clab 2024  df-cleq 2030  df-clel 2033  df-nfc 2164  df-in 2918  df-ss 2925  df-br 3756  df-opab 3810  df-cnv 4296 This theorem is referenced by:  cnvsng  4749  cores2  4776  suppssof1  5670  2ndval2  5725  2nd1st  5748  cnvf1olem  5787  brtpos2  5807  dftpos4  5819  tpostpos  5820  tposf12  5825  xpcomco  6236
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