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Theorem cnveqd 4803
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 4801 . 2 (𝐴 = 𝐵𝐴 = 𝐵)
31, 2syl 14 1 (𝜑𝐴 = 𝐵)
Colors of variables: wff set class
Syntax hints:  wi 4   = wceq 1353  ccnv 4625
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-io 709  ax-5 1447  ax-7 1448  ax-gen 1449  ax-ie1 1493  ax-ie2 1494  ax-8 1504  ax-10 1505  ax-11 1506  ax-i12 1507  ax-bndl 1509  ax-4 1510  ax-17 1526  ax-i9 1530  ax-ial 1534  ax-i5r 1535  ax-ext 2159
This theorem depends on definitions:  df-bi 117  df-nf 1461  df-sb 1763  df-clab 2164  df-cleq 2170  df-clel 2173  df-nfc 2308  df-in 3135  df-ss 3142  df-br 4004  df-opab 4065  df-cnv 4634
This theorem is referenced by:  cnvsng  5114  cores2  5141  suppssof1  6099  2ndval2  6156  2nd1st  6180  cnvf1olem  6224  brtpos2  6251  dftpos4  6263  tpostpos  6264  tposf12  6269  xpcomco  6825  infeq123d  7014  fsumcnv  11444  fprodcnv  11632  ennnfonelemf1  12418  xpsval  12770  grpinvcnv  12937  grplactcnv  12971  eqglact  13082  isunitd  13273  txswaphmeolem  13790
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