Theorem cnveqi 4930

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 4929	. 2 |- ( A = B -> `' A = `' B )
3	1, 2	ax-mp 5	1 |- `' A = `' B

Syntax hints:   = wceq 1398   `'ccnv 4748

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 2214

This theorem depends on definitions:  df-bi 117  df-nf 1510  df-sb 1812  df-clab 2219  df-cleq 2225  df-clel 2228  df-nfc 2373  df-in 3217  df-ss 3224  df-br 4110  df-opab 4172  df-cnv 4757

This theorem is referenced by:  mptcnv  5165  cnvxp  5181  xp0  5182  imainrect  5208  cnvcnv  5215  mptpreima  5256  co01  5277  coi2  5279  cocnvres  5287  fcoi1  5547  fun11iun  5635  f1ocnvd  6257  cnvoprab  6430  f1od2  6431  mapsncnv  6930  sbthlemi8  7234  caseinj  7380  djuinj  7397  fisumcom2  12124  fprodcom2fi  12312