Theorem cnveqd 4843

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 4841	. 2 |- ( A = B -> `' A = `' B )
3	1, 2	syl 14	1 |- ( ph -> `' A = `' B )

Syntax hints:   -> wi 4   = wceq 1364   `'ccnv 4663

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 710  ax-5 1461  ax-7 1462  ax-gen 1463  ax-ie1 1507  ax-ie2 1508  ax-8 1518  ax-10 1519  ax-11 1520  ax-i12 1521  ax-bndl 1523  ax-4 1524  ax-17 1540  ax-i9 1544  ax-ial 1548  ax-i5r 1549  ax-ext 2178

This theorem depends on definitions:  df-bi 117  df-nf 1475  df-sb 1777  df-clab 2183  df-cleq 2189  df-clel 2192  df-nfc 2328  df-in 3163  df-ss 3170  df-br 4035  df-opab 4096  df-cnv 4672

This theorem is referenced by:  cnvsng  5156  cores2  5183  suppssof1  6157  2ndval2  6223  2nd1st  6247  cnvf1olem  6291  brtpos2  6318  dftpos4  6330  tpostpos  6331  tposf12  6336  xpcomco  6894  infeq123d  7091  fsumcnv  11619  fprodcnv  11807  ennnfonelemf1  12660  strslfv3  12749  xpsval  13054  grpinvcnv  13270  grplactcnv  13304  eqglact  13431  isunitd  13738  znval  14268  znle2  14284  txswaphmeolem  14640