Theorem cnveqi 4957

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 4956	. 2 |- ( A = B -> `' A = `' B )
3	1, 2	ax-mp 5	1 |- `' A = `' B

This proof depends on syntax axioms:   = wceq 1402   `'ccnv 4775

This proof depends on 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 proof 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 4132  df-opab 4194  df-cnv 4784

This theorem is used by:  mptcnv  5193  cnvxp  5209  xp0  5210  imainrect  5236  cnvcnv  5243  mptpreima  5284  co01  5305  coi2  5307  cocnvres  5315  fcoi1  5575  fun11iun  5663  f1ocnvd  6295  cnvoprab  6474  f1od2  6475  mapsncnv  6981  sbthlemi8  7286  caseinj  7435  djuinj  7452  fisumcom2  12230  fprodcom2fi  12418  ballotfilemrinv  13335