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Theorem rmobii 2731
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 2730 1  |-  ( E* x  e.  A ph  <->  E* x  e.  A ps )
Colors of variables: wff set class
Syntax hints:    <-> wb 176    e. wcel 1684   E*wrmo 2546
This theorem is referenced by:  reuxfr2d  4557  brdom7disj  8156  reuxfr3d  23138  cvmlift2lem13  23846  2reu5a  27955
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1533  ax-5 1544  ax-17 1603  ax-9 1635  ax-8 1643  ax-11 1715
This theorem depends on definitions:  df-bi 177  df-an 360  df-tru 1310  df-ex 1529  df-nf 1532  df-eu 2147  df-mo 2148  df-rmo 2551
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