Theorem cnveqi 4950

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 4949	. 2 |- ( A = B -> `' A = `' B )
3	1, 2	ax-mp 5	1 |- `' A = `' B

Syntax hints:   = wceq 1402   `'ccnv 4768

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 721  ax-5 1500  ax-7 1501  ax-gen 1502  ax-ie1 1546  ax-ie2 1547  ax-8 1557  ax-10 1558  ax-11 1559  ax-i12 1560  ax-bndl 1562  ax-4 1563  ax-17 1579  ax-i9 1583  ax-ial 1587  ax-i5r 1588  ax-ext 2220

This theorem depends on definitions:  df-bi 117  df-nf 1514  df-sb 1816  df-clab 2225  df-cleq 2231  df-clel 2234  df-nfc 2381  df-in 3226  df-ss 3233  df-br 4126  df-opab 4188  df-cnv 4777

This theorem is referenced by:  mptcnv  5185  cnvxp  5201  xp0  5202  imainrect  5228  cnvcnv  5235  mptpreima  5276  co01  5297  coi2  5299  cocnvres  5307  fcoi1  5567  fun11iun  5655  f1ocnvd  6282  cnvoprab  6460  f1od2  6461  mapsncnv  6967  sbthlemi8  7271  caseinj  7419  djuinj  7436  fisumcom2  12183  fprodcom2fi  12371  ballotfilemrinv  13255