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

Theorem rmobii 2744
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 10 . 2  |-  ( x  e.  A  ->  ( ph 
<->  ps ) )
32rmobiia 2743 1  |-  ( E* x  e.  A ph  <->  E* x  e.  A ps )
Colors of variables: wff set class
Syntax hints:    <-> wb 176    e. wcel 1696   E*wrmo 2559
This theorem is referenced by:  reuxfr2d  4573  brdom7disj  8172  reuxfr3d  23154  cvmlift2lem13  23861  2reu5a  28058
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1536  ax-5 1547  ax-17 1606  ax-9 1644  ax-8 1661  ax-11 1727
This theorem depends on definitions:  df-bi 177  df-an 360  df-tru 1310  df-ex 1532  df-nf 1535  df-eu 2160  df-mo 2161  df-rmo 2564
  Copyright terms: Public domain W3C validator