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

Theorem reubida 3040
 Description: Formula-building rule for restricted existential quantifier (deduction rule). (Contributed by Mario Carneiro, 19-Nov-2016.)
Hypotheses
Ref Expression
reubida.1
reubida.2
Assertion
Ref Expression
reubida

Proof of Theorem reubida
StepHypRef Expression
1 reubida.1 . . 3
2 reubida.2 . . . 4
32pm5.32da 641 . . 3
41, 3eubid 2302 . 2
5 df-reu 2814 . 2
6 df-reu 2814 . 2
74, 5, 63bitr4g 288 1
 Colors of variables: wff setvar class Syntax hints:  ->wi 4  <->wb 184  /\wa 369  F/wnf 1616  e.wcel 1818  E!weu 2282  E!wreu 2809 This theorem is referenced by:  reubidva  3041  reuan  32185 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-12 1854 This theorem depends on definitions:  df-bi 185  df-an 371  df-ex 1613  df-nf 1617  df-eu 2286  df-reu 2814
 Copyright terms: Public domain W3C validator