Theorem cnveqd 4951

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 4949	. 2 |- ( A = B -> `' A = `' B )
3	1, 2	syl 14	1 |- ( ph -> `' A = `' B )

Syntax hints:   -> wi 4   = wceq 1402   `'ccnv 4768

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 721  ax-5 1500  ax-7 1501  ax-gen 1502  ax-ie1 1546  ax-ie2 1547  ax-8 1557  ax-10 1558  ax-11 1559  ax-i12 1560  ax-bndl 1562  ax-4 1563  ax-17 1579  ax-i9 1583  ax-ial 1587  ax-i5r 1588  ax-ext 2220

This theorem depends on definitions:  df-bi 117  df-nf 1514  df-sb 1816  df-clab 2225  df-cleq 2231  df-clel 2234  df-nfc 2381  df-in 3226  df-ss 3233  df-br 4126  df-opab 4188  df-cnv 4777

This theorem is referenced by:  cnvsng  5268  cores2  5295  f1o3d  6288  suppssof1  6310  2ndval2  6380  2nd1st  6404  cnvf1olem  6450  brtpos2  6512  dftpos4  6524  tpostpos  6525  tposf12  6530  xpcomco  7114  infeq123d  7346  fsumcnv  12182  fprodcnv  12370  ennnfonelemf1  13287  strslfv3  13376  grpinvcnv  13850  grplactcnv  13884  eqglact  14005  xpsval  14178  isunitd  14386  znval  14943  znle2  14959  txswaphmeolem  15344