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

Theorem rmobii 3001
Description: Formula-building rule for restricted existential quantifier (inference rule). (Contributed by NM, 16-Jun-2017.)
Hypothesis
Ref Expression
rmobii.1  |-  ( ph  <->  ps )
Assertion
Ref Expression
rmobii  |-  ( E* x  e.  A  ph  <->  E* x  e.  A  ps )

Proof of Theorem rmobii
StepHypRef Expression
1 rmobii.1 . . 3  |-  ( ph  <->  ps )
21a1i 11 . 2  |-  ( x  e.  A  ->  ( ph 
<->  ps ) )
32rmobiia 3000 1  |-  ( E* x  e.  A  ph  <->  E* x  e.  A  ps )
Colors of variables: wff setvar class
Syntax hints:    <-> wb 186    e. wcel 1844   E*wrmo 2759
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1641  ax-4 1654  ax-5 1727  ax-6 1773  ax-7 1816  ax-12 1880
This theorem depends on definitions:  df-bi 187  df-an 371  df-tru 1410  df-ex 1636  df-nf 1640  df-eu 2244  df-mo 2245  df-rmo 2764
This theorem is referenced by:  reuxfr2d  4616  brdom7disj  8943  reuxfr3d  27816  cvmlift2lem13  29625  2reu5a  37563
  Copyright terms: Public domain W3C validator