Theorem cnveqi 4799

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 4798	. 2 |- ( A = B -> `' A = `' B )
3	1, 2	ax-mp 5	1 |- `' A = `' B

Syntax hints:   = wceq 1353   `'ccnv 4623

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 4002  df-opab 4063  df-cnv 4632

This theorem is referenced by:  mptcnv  5028  cnvxp  5044  xp0  5045  imainrect  5071  cnvcnv  5078  mptpreima  5119  co01  5140  coi2  5142  cocnvres  5150  fcoi1  5393  fun11iun  5479  f1ocnvd  6068  cnvoprab  6230  f1od2  6231  mapsncnv  6690  sbthlemi8  6958  caseinj  7083  djuinj  7100  fisumcom2  11437  fprodcom2fi  11625