Theorem cnveqd 4931

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 4929	. 2 |- ( A = B -> `' A = `' B )
3	1, 2	syl 14	1 |- ( ph -> `' A = `' B )

Syntax hints:   -> wi 4   = wceq 1398   `'ccnv 4748

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 2214

This theorem depends on definitions:  df-bi 117  df-nf 1510  df-sb 1812  df-clab 2219  df-cleq 2225  df-clel 2228  df-nfc 2373  df-in 3217  df-ss 3224  df-br 4110  df-opab 4172  df-cnv 4757

This theorem is referenced by:  cnvsng  5248  cores2  5275  suppssof1  6284  2ndval2  6350  2nd1st  6374  cnvf1olem  6420  brtpos2  6482  dftpos4  6494  tpostpos  6495  tposf12  6500  xpcomco  7077  infeq123d  7307  fsumcnv  12123  fprodcnv  12311  ennnfonelemf1  13169  strslfv3  13258  xpsval  13565  grpinvcnv  13781  grplactcnv  13815  eqglact  13942  isunitd  14251  znval  14784  znle2  14800  txswaphmeolem  15185