Theorem cnveqi 4842

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 4841	. 2 |- ( A = B -> `' A = `' B )
3	1, 2	ax-mp 5	1 |- `' A = `' B

Syntax hints:   = wceq 1364   `'ccnv 4663

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 710  ax-5 1461  ax-7 1462  ax-gen 1463  ax-ie1 1507  ax-ie2 1508  ax-8 1518  ax-10 1519  ax-11 1520  ax-i12 1521  ax-bndl 1523  ax-4 1524  ax-17 1540  ax-i9 1544  ax-ial 1548  ax-i5r 1549  ax-ext 2178

This theorem depends on definitions:  df-bi 117  df-nf 1475  df-sb 1777  df-clab 2183  df-cleq 2189  df-clel 2192  df-nfc 2328  df-in 3163  df-ss 3170  df-br 4035  df-opab 4096  df-cnv 4672

This theorem is referenced by:  mptcnv  5073  cnvxp  5089  xp0  5090  imainrect  5116  cnvcnv  5123  mptpreima  5164  co01  5185  coi2  5187  cocnvres  5195  fcoi1  5441  fun11iun  5528  f1ocnvd  6129  cnvoprab  6301  f1od2  6302  mapsncnv  6763  sbthlemi8  7039  caseinj  7164  djuinj  7181  fisumcom2  11620  fprodcom2fi  11808