Theorem cnveqi 4722

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 4721	. 2 |- ( A = B -> `' A = `' B )
3	1, 2	ax-mp 5	1 |- `' A = `' B

Syntax hints:   = wceq 1332   `'ccnv 4546

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 699  ax-5 1424  ax-7 1425  ax-gen 1426  ax-ie1 1470  ax-ie2 1471  ax-8 1483  ax-10 1484  ax-11 1485  ax-i12 1486  ax-bndl 1487  ax-4 1488  ax-17 1507  ax-i9 1511  ax-ial 1515  ax-i5r 1516  ax-ext 2122

This theorem depends on definitions:  df-bi 116  df-nf 1438  df-sb 1737  df-clab 2127  df-cleq 2133  df-clel 2136  df-nfc 2271  df-in 3082  df-ss 3089  df-br 3938  df-opab 3998  df-cnv 4555

This theorem is referenced by:  mptcnv  4949  cnvxp  4965  xp0  4966  imainrect  4992  cnvcnv  4999  mptpreima  5040  co01  5061  coi2  5063  cocnvres  5071  fcoi1  5311  fun11iun  5396  f1ocnvd  5980  cnvoprab  6139  f1od2  6140  mapsncnv  6597  sbthlemi8  6860  caseinj  6982  djuinj  6999  fisumcom2  11239