Theorem cnveqd 4815

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

Step	Hyp	Ref	Expression
1		cnveqd.1	. 2 |- ( ph -> A = B )
2		cnveq 4813	. 2 |- ( A = B -> `' A = `' B )
3	1, 2	syl 14	1 |- ( ph -> `' A = `' B )

Syntax hints:   -> wi 4   = wceq 1363   `'ccnv 4637

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 710  ax-5 1457  ax-7 1458  ax-gen 1459  ax-ie1 1503  ax-ie2 1504  ax-8 1514  ax-10 1515  ax-11 1516  ax-i12 1517  ax-bndl 1519  ax-4 1520  ax-17 1536  ax-i9 1540  ax-ial 1544  ax-i5r 1545  ax-ext 2169

This theorem depends on definitions:  df-bi 117  df-nf 1471  df-sb 1773  df-clab 2174  df-cleq 2180  df-clel 2183  df-nfc 2318  df-in 3147  df-ss 3154  df-br 4016  df-opab 4077  df-cnv 4646

This theorem is referenced by:  cnvsng  5126  cores2  5153  suppssof1  6114  2ndval2  6171  2nd1st  6195  cnvf1olem  6239  brtpos2  6266  dftpos4  6278  tpostpos  6279  tposf12  6284  xpcomco  6840  infeq123d  7029  fsumcnv  11459  fprodcnv  11647  ennnfonelemf1  12433  xpsval  12790  grpinvcnv  12965  grplactcnv  12999  eqglact  13117  isunitd  13354  txswaphmeolem  14116