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

Theorem rexeqbii 2736
 Description: Equality deduction for restricted existential quantifier, changing both formula and quantifier domain. Inference form. (Contributed by David Moews, 1-May-2017.)
Hypotheses
Ref Expression
raleqbii.1
raleqbii.2
Assertion
Ref Expression
rexeqbii

Proof of Theorem rexeqbii
StepHypRef Expression
1 raleqbii.1 . . . 4
21eleq2i 2500 . . 3
3 raleqbii.2 . . 3
42, 3anbi12i 679 . 2
54rexbii2 2734 1
 Colors of variables: wff set class Syntax hints:   wb 177   wceq 1652   wcel 1725  wrex 2706 This theorem is referenced by:  bnj882  29297 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-11 1761  ax-ext 2417 This theorem depends on definitions:  df-bi 178  df-an 361  df-ex 1551  df-cleq 2429  df-clel 2432  df-rex 2711
 Copyright terms: Public domain W3C validator