Metamath Proof Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  MPE Home  >  Th. List  >  rmoeqd Structured version   Unicode version

Theorem rmoeqd 2915
 Description: Equality deduction for restricted uniqueness quantifier. (Contributed by Alexander van der Vekens, 17-Jun-2017.)
Hypothesis
Ref Expression
raleqd.1
Assertion
Ref Expression
rmoeqd
Distinct variable groups:   ,   ,
Allowed substitution hints:   ()   ()

Proof of Theorem rmoeqd
StepHypRef Expression
1 rmoeq1 2907 . 2
2 raleqd.1 . . 3
32rmobidv 2897 . 2
41, 3bitrd 245 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 177   wceq 1652  wrmo 2708 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2417 This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-eu 2285  df-mo 2286  df-cleq 2429  df-clel 2432  df-nfc 2561  df-rmo 2713
 Copyright terms: Public domain W3C validator