Theorem cnveqd 4898

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 4896	. 2 |- ( A = B -> `' A = `' B )
3	1, 2	syl 14	1 |- ( ph -> `' A = `' B )

Syntax hints:   -> wi 4   = wceq 1395   `'ccnv 4718

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 714  ax-5 1493  ax-7 1494  ax-gen 1495  ax-ie1 1539  ax-ie2 1540  ax-8 1550  ax-10 1551  ax-11 1552  ax-i12 1553  ax-bndl 1555  ax-4 1556  ax-17 1572  ax-i9 1576  ax-ial 1580  ax-i5r 1581  ax-ext 2211

This theorem depends on definitions:  df-bi 117  df-nf 1507  df-sb 1809  df-clab 2216  df-cleq 2222  df-clel 2225  df-nfc 2361  df-in 3203  df-ss 3210  df-br 4084  df-opab 4146  df-cnv 4727

This theorem is referenced by:  cnvsng  5214  cores2  5241  suppssof1  6236  2ndval2  6302  2nd1st  6326  cnvf1olem  6370  brtpos2  6397  dftpos4  6409  tpostpos  6410  tposf12  6415  xpcomco  6985  infeq123d  7183  fsumcnv  11948  fprodcnv  12136  ennnfonelemf1  12989  strslfv3  13078  xpsval  13385  grpinvcnv  13601  grplactcnv  13635  eqglact  13762  isunitd  14070  znval  14600  znle2  14616  txswaphmeolem  14994