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Theorem cnveqd 4804
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 4802 . 2 (𝐴 = 𝐵𝐴 = 𝐵)
31, 2syl 14 1 (𝜑𝐴 = 𝐵)
Colors of variables: wff set class
Syntax hints:  wi 4   = wceq 1353  ccnv 4626
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 3136  df-ss 3143  df-br 4005  df-opab 4066  df-cnv 4635
This theorem is referenced by:  cnvsng  5115  cores2  5142  suppssof1  6100  2ndval2  6157  2nd1st  6181  cnvf1olem  6225  brtpos2  6252  dftpos4  6264  tpostpos  6265  tposf12  6270  xpcomco  6826  infeq123d  7015  fsumcnv  11445  fprodcnv  11633  ennnfonelemf1  12419  xpsval  12771  grpinvcnv  12938  grplactcnv  12972  eqglact  13084  isunitd  13275  txswaphmeolem  13823
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