Theorem cnveqi 4871

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 4870	. 2 |- ( A = B -> `' A = `' B )
3	1, 2	ax-mp 5	1 |- `' A = `' B

Syntax hints:   = wceq 1373   `'ccnv 4692

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 711  ax-5 1471  ax-7 1472  ax-gen 1473  ax-ie1 1517  ax-ie2 1518  ax-8 1528  ax-10 1529  ax-11 1530  ax-i12 1531  ax-bndl 1533  ax-4 1534  ax-17 1550  ax-i9 1554  ax-ial 1558  ax-i5r 1559  ax-ext 2189

This theorem depends on definitions:  df-bi 117  df-nf 1485  df-sb 1787  df-clab 2194  df-cleq 2200  df-clel 2203  df-nfc 2339  df-in 3180  df-ss 3187  df-br 4060  df-opab 4122  df-cnv 4701

This theorem is referenced by:  mptcnv  5104  cnvxp  5120  xp0  5121  imainrect  5147  cnvcnv  5154  mptpreima  5195  co01  5216  coi2  5218  cocnvres  5226  fcoi1  5478  fun11iun  5565  f1ocnvd  6171  cnvoprab  6343  f1od2  6344  mapsncnv  6805  sbthlemi8  7092  caseinj  7217  djuinj  7234  fisumcom2  11864  fprodcom2fi  12052