Intuitionistic Logic Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  ILE Home  >  Th. List  >  cdeqab1 Unicode version

Theorem cdeqab1 2901
 Description: Distribute conditional equality over abstraction. (Contributed by Mario Carneiro, 11-Aug-2016.)
Hypothesis
Ref Expression
cdeqnot.1 CondEq
Assertion
Ref Expression
cdeqab1 CondEq
Distinct variable groups:   ,   ,
Allowed substitution hints:   ()   ()

Proof of Theorem cdeqab1
StepHypRef Expression
1 cdeqnot.1 . . . 4 CondEq
21cdeqri 2895 . . 3
32cbvabv 2264 . 2
43cdeqth 2896 1 CondEq
 Colors of variables: wff set class Syntax hints:   wb 104   wceq 1331  cab 2125  CondEqwcdeq 2892 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 698  ax-5 1423  ax-7 1424  ax-gen 1425  ax-ie1 1469  ax-ie2 1470  ax-8 1482  ax-10 1483  ax-11 1484  ax-i12 1485  ax-bndl 1486  ax-4 1487  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-i5r 1515  ax-ext 2121 This theorem depends on definitions:  df-bi 116  df-nf 1437  df-sb 1736  df-clab 2126  df-cleq 2132  df-cdeq 2893 This theorem is referenced by: (None)
 Copyright terms: Public domain W3C validator