Theorem cnveqd 4912

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 4910	. 2 |- ( A = B -> `' A = `' B )
3	1, 2	syl 14	1 |- ( ph -> `' A = `' B )

Syntax hints:   -> wi 4   = wceq 1398   `'ccnv 4730

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 2213

This theorem depends on definitions:  df-bi 117  df-nf 1510  df-sb 1811  df-clab 2218  df-cleq 2224  df-clel 2227  df-nfc 2364  df-in 3207  df-ss 3214  df-br 4094  df-opab 4156  df-cnv 4739

This theorem is referenced by:  cnvsng  5229  cores2  5256  suppssof1  6262  2ndval2  6328  2nd1st  6352  cnvf1olem  6398  brtpos2  6460  dftpos4  6472  tpostpos  6473  tposf12  6478  xpcomco  7053  infeq123d  7275  fsumcnv  12078  fprodcnv  12266  ennnfonelemf1  13119  strslfv3  13208  xpsval  13515  grpinvcnv  13731  grplactcnv  13765  eqglact  13892  isunitd  14201  znval  14732  znle2  14748  txswaphmeolem  15131