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Theorem cnveqd 4787
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 4785 . 2 (𝐴 = 𝐵𝐴 = 𝐵)
31, 2syl 14 1 (𝜑𝐴 = 𝐵)
Colors of variables: wff set class
Syntax hints:  wi 4   = wceq 1348  ccnv 4610
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 704  ax-5 1440  ax-7 1441  ax-gen 1442  ax-ie1 1486  ax-ie2 1487  ax-8 1497  ax-10 1498  ax-11 1499  ax-i12 1500  ax-bndl 1502  ax-4 1503  ax-17 1519  ax-i9 1523  ax-ial 1527  ax-i5r 1528  ax-ext 2152
This theorem depends on definitions:  df-bi 116  df-nf 1454  df-sb 1756  df-clab 2157  df-cleq 2163  df-clel 2166  df-nfc 2301  df-in 3127  df-ss 3134  df-br 3990  df-opab 4051  df-cnv 4619
This theorem is referenced by:  cnvsng  5096  cores2  5123  suppssof1  6078  2ndval2  6135  2nd1st  6159  cnvf1olem  6203  brtpos2  6230  dftpos4  6242  tpostpos  6243  tposf12  6248  xpcomco  6804  infeq123d  6993  fsumcnv  11400  fprodcnv  11588  ennnfonelemf1  12373  grpinvcnv  12767  txswaphmeolem  13114
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