Theorem cnveqd 4906

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 4904	. 2 |- ( A = B -> `' A = `' B )
3	1, 2	syl 14	1 |- ( ph -> `' A = `' B )

Syntax hints:   -> wi 4   = wceq 1397   `'ccnv 4724

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 716  ax-5 1495  ax-7 1496  ax-gen 1497  ax-ie1 1541  ax-ie2 1542  ax-8 1552  ax-10 1553  ax-11 1554  ax-i12 1555  ax-bndl 1557  ax-4 1558  ax-17 1574  ax-i9 1578  ax-ial 1582  ax-i5r 1583  ax-ext 2213

This theorem depends on definitions:  df-bi 117  df-nf 1509  df-sb 1811  df-clab 2218  df-cleq 2224  df-clel 2227  df-nfc 2363  df-in 3206  df-ss 3213  df-br 4089  df-opab 4151  df-cnv 4733

This theorem is referenced by:  cnvsng  5222  cores2  5249  suppssof1  6252  2ndval2  6318  2nd1st  6342  cnvf1olem  6388  brtpos2  6416  dftpos4  6428  tpostpos  6429  tposf12  6434  xpcomco  7009  infeq123d  7214  fsumcnv  11997  fprodcnv  12185  ennnfonelemf1  13038  strslfv3  13127  xpsval  13434  grpinvcnv  13650  grplactcnv  13684  eqglact  13811  isunitd  14119  znval  14649  znle2  14665  txswaphmeolem  15043