ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  cnveqd Unicode version

Theorem cnveqd 4533
Description: Equality deduction for converse. (Contributed by NM, 6-Dec-2013.)
Hypothesis
Ref Expression
cnveqd.1  |-  ( ph  ->  A  =  B )
Assertion
Ref Expression
cnveqd  |-  ( ph  ->  `' A  =  `' B )

Proof of Theorem cnveqd
StepHypRef Expression
1 cnveqd.1 . 2  |-  ( ph  ->  A  =  B )
2 cnveq 4531 . 2  |-  ( A  =  B  ->  `' A  =  `' B
)
31, 2syl 14 1  |-  ( ph  ->  `' A  =  `' B )
Colors of variables: wff set class
Syntax hints:    -> wi 4    = wceq 1285   `'ccnv 4364
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-io 663  ax-5 1377  ax-7 1378  ax-gen 1379  ax-ie1 1423  ax-ie2 1424  ax-8 1436  ax-10 1437  ax-11 1438  ax-i12 1439  ax-bndl 1440  ax-4 1441  ax-17 1460  ax-i9 1464  ax-ial 1468  ax-i5r 1469  ax-ext 2064
This theorem depends on definitions:  df-bi 115  df-nf 1391  df-sb 1687  df-clab 2069  df-cleq 2075  df-clel 2078  df-nfc 2209  df-in 2980  df-ss 2987  df-br 3788  df-opab 3842  df-cnv 4373
This theorem is referenced by:  cnvsng  4830  cores2  4857  suppssof1  5753  2ndval2  5808  2nd1st  5831  cnvf1olem  5870  brtpos2  5894  dftpos4  5906  tpostpos  5907  tposf12  5912  xpcomco  6360  infeq123d  6478
  Copyright terms: Public domain W3C validator