Theorem cnveqd 4936

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 4934	. 2 |- ( A = B -> `' A = `' B )
3	1, 2	syl 14	1 |- ( ph -> `' A = `' B )

Syntax hints:   -> wi 4   = wceq 1398   `'ccnv 4753

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 717  ax-5 1496  ax-7 1497  ax-gen 1498  ax-ie1 1542  ax-ie2 1543  ax-8 1553  ax-10 1554  ax-11 1555  ax-i12 1556  ax-bndl 1558  ax-4 1559  ax-17 1575  ax-i9 1579  ax-ial 1583  ax-i5r 1584  ax-ext 2216

This theorem depends on definitions:  df-bi 117  df-nf 1510  df-sb 1812  df-clab 2221  df-cleq 2227  df-clel 2230  df-nfc 2375  df-in 3220  df-ss 3227  df-br 4115  df-opab 4177  df-cnv 4762

This theorem is referenced by:  cnvsng  5253  cores2  5280  f1o3d  6271  suppssof1  6293  2ndval2  6363  2nd1st  6387  cnvf1olem  6433  brtpos2  6495  dftpos4  6507  tpostpos  6508  tposf12  6513  xpcomco  7090  infeq123d  7320  fsumcnv  12148  fprodcnv  12336  ennnfonelemf1  13253  strslfv3  13342  grpinvcnv  13823  grplactcnv  13857  eqglact  13978  xpsval  14143  isunitd  14351  znval  14910  znle2  14926  txswaphmeolem  15311