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  6242  2ndval2  6308  2nd1st  6332  cnvf1olem  6376  brtpos2  6403  dftpos4  6415  tpostpos  6416  tposf12  6421  xpcomco  6993  infeq123d  7194  fsumcnv  11964  fprodcnv  12152  ennnfonelemf1  13005  strslfv3  13094  xpsval  13401  grpinvcnv  13617  grplactcnv  13651  eqglact  13778  isunitd  14086  znval  14616  znle2  14632  txswaphmeolem  15010