Theorem cnveqi 4761

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 4760	. 2 |- ( A = B -> `' A = `' B )
3	1, 2	ax-mp 5	1 |- `' A = `' B

Syntax hints:   = wceq 1335   `'ccnv 4585

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 699  ax-5 1427  ax-7 1428  ax-gen 1429  ax-ie1 1473  ax-ie2 1474  ax-8 1484  ax-10 1485  ax-11 1486  ax-i12 1487  ax-bndl 1489  ax-4 1490  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-i5r 1515  ax-ext 2139

This theorem depends on definitions:  df-bi 116  df-nf 1441  df-sb 1743  df-clab 2144  df-cleq 2150  df-clel 2153  df-nfc 2288  df-in 3108  df-ss 3115  df-br 3966  df-opab 4026  df-cnv 4594

This theorem is referenced by:  mptcnv  4988  cnvxp  5004  xp0  5005  imainrect  5031  cnvcnv  5038  mptpreima  5079  co01  5100  coi2  5102  cocnvres  5110  fcoi1  5350  fun11iun  5435  f1ocnvd  6022  cnvoprab  6181  f1od2  6182  mapsncnv  6640  sbthlemi8  6908  caseinj  7033  djuinj  7050  fisumcom2  11335  fprodcom2fi  11523