Theorem cnveqd 4839

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 4837	. 2 |- ( A = B -> `' A = `' B )
3	1, 2	syl 14	1 |- ( ph -> `' A = `' B )

Syntax hints:   -> wi 4   = wceq 1364   `'ccnv 4659

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 1458  ax-7 1459  ax-gen 1460  ax-ie1 1504  ax-ie2 1505  ax-8 1515  ax-10 1516  ax-11 1517  ax-i12 1518  ax-bndl 1520  ax-4 1521  ax-17 1537  ax-i9 1541  ax-ial 1545  ax-i5r 1546  ax-ext 2175

This theorem depends on definitions:  df-bi 117  df-nf 1472  df-sb 1774  df-clab 2180  df-cleq 2186  df-clel 2189  df-nfc 2325  df-in 3160  df-ss 3167  df-br 4031  df-opab 4092  df-cnv 4668

This theorem is referenced by:  cnvsng  5152  cores2  5179  suppssof1  6150  2ndval2  6211  2nd1st  6235  cnvf1olem  6279  brtpos2  6306  dftpos4  6318  tpostpos  6319  tposf12  6324  xpcomco  6882  infeq123d  7077  fsumcnv  11583  fprodcnv  11771  ennnfonelemf1  12578  xpsval  12938  grpinvcnv  13143  grplactcnv  13177  eqglact  13298  isunitd  13605  znval  14135  znle2  14151  txswaphmeolem  14499