Theorem cnveqi 4935

Description: Equality inference for converse. (Contributed by NM, 23-Dec-2008.)

Hypothesis

Ref	Expression
cnveqi.1	|- A = B

Assertion

Ref	Expression
cnveqi	|- `' A = `' B

Proof of Theorem cnveqi

Step	Hyp	Ref	Expression
1		cnveqi.1	. 2 |- A = B
2		cnveq 4934	. 2 |- ( A = B -> `' A = `' B )
3	1, 2	ax-mp 5	1 |- `' A = `' B

Syntax hints:   = wceq 1398   `'ccnv 4753

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 2216

This theorem depends on definitions:  df-bi 117  df-nf 1510  df-sb 1812  df-clab 2221  df-cleq 2227  df-clel 2230  df-nfc 2375  df-in 3220  df-ss 3227  df-br 4115  df-opab 4177  df-cnv 4762

This theorem is referenced by:  mptcnv  5170  cnvxp  5186  xp0  5187  imainrect  5213  cnvcnv  5220  mptpreima  5261  co01  5282  coi2  5284  cocnvres  5292  fcoi1  5552  fun11iun  5640  f1ocnvd  6265  cnvoprab  6443  f1od2  6444  mapsncnv  6943  sbthlemi8  7247  caseinj  7393  djuinj  7410  fisumcom2  12149  fprodcom2fi  12337  ballotfilemrinv  13221