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

Theorem rabeqbidv 2597
 Description: Equality of restricted class abstractions. (Contributed by Jeff Madsen, 1-Dec-2009.)
Hypotheses
Ref Expression
rabeqbidv.1
rabeqbidv.2
Assertion
Ref Expression
rabeqbidv
Distinct variable groups:   ,   ,   ,
Allowed substitution hints:   ()   ()

Proof of Theorem rabeqbidv
StepHypRef Expression
1 rabeqbidv.1 . . 3
2 rabeq 2596 . . 3
31, 2syl 14 . 2
4 rabeqbidv.2 . . 3
54rabbidv 2594 . 2
63, 5eqtrd 2114 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 103   wceq 1285  crab 2353 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-tru 1288  df-nf 1391  df-sb 1687  df-clab 2069  df-cleq 2075  df-clel 2078  df-nfc 2209  df-ral 2354  df-rab 2358 This theorem is referenced by:  mpt2xopoveq  5883  supeq123d  6453
 Copyright terms: Public domain W3C validator