Theorem cnveqi 4802

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 4801	. 2 |- ( A = B -> `' A = `' B )
3	1, 2	ax-mp 5	1 |- `' A = `' B

Syntax hints:   = wceq 1353   `'ccnv 4625

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 709  ax-5 1447  ax-7 1448  ax-gen 1449  ax-ie1 1493  ax-ie2 1494  ax-8 1504  ax-10 1505  ax-11 1506  ax-i12 1507  ax-bndl 1509  ax-4 1510  ax-17 1526  ax-i9 1530  ax-ial 1534  ax-i5r 1535  ax-ext 2159

This theorem depends on definitions:  df-bi 117  df-nf 1461  df-sb 1763  df-clab 2164  df-cleq 2170  df-clel 2173  df-nfc 2308  df-in 3135  df-ss 3142  df-br 4004  df-opab 4065  df-cnv 4634

This theorem is referenced by:  mptcnv  5031  cnvxp  5047  xp0  5048  imainrect  5074  cnvcnv  5081  mptpreima  5122  co01  5143  coi2  5145  cocnvres  5153  fcoi1  5396  fun11iun  5482  f1ocnvd  6072  cnvoprab  6234  f1od2  6235  mapsncnv  6694  sbthlemi8  6962  caseinj  7087  djuinj  7104  fisumcom2  11445  fprodcom2fi  11633