Theorem cnveqd 4855

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 4853	. 2 |- ( A = B -> `' A = `' B )
3	1, 2	syl 14	1 |- ( ph -> `' A = `' B )

Syntax hints:   -> wi 4   = wceq 1373   `'ccnv 4675

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 711  ax-5 1470  ax-7 1471  ax-gen 1472  ax-ie1 1516  ax-ie2 1517  ax-8 1527  ax-10 1528  ax-11 1529  ax-i12 1530  ax-bndl 1532  ax-4 1533  ax-17 1549  ax-i9 1553  ax-ial 1557  ax-i5r 1558  ax-ext 2187

This theorem depends on definitions:  df-bi 117  df-nf 1484  df-sb 1786  df-clab 2192  df-cleq 2198  df-clel 2201  df-nfc 2337  df-in 3172  df-ss 3179  df-br 4046  df-opab 4107  df-cnv 4684

This theorem is referenced by:  cnvsng  5169  cores2  5196  suppssof1  6178  2ndval2  6244  2nd1st  6268  cnvf1olem  6312  brtpos2  6339  dftpos4  6351  tpostpos  6352  tposf12  6357  xpcomco  6923  infeq123d  7120  fsumcnv  11781  fprodcnv  11969  ennnfonelemf1  12822  strslfv3  12911  xpsval  13217  grpinvcnv  13433  grplactcnv  13467  eqglact  13594  isunitd  13901  znval  14431  znle2  14447  txswaphmeolem  14825