Theorem rmobii 3133

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

Step	Hyp	Ref	Expression
1		rmobii.1	. . 3 |- ( ph <-> ps )
2	1	a1i 11	. 2 |- ( x e. A -> ( ph <-> ps ) )
3	2	rmobiia 3132	1 |- ( E* x e. A ph <-> E* x e. A ps )

Syntax hints:   <-> wb 196   e. wcel 1990   E*wrmo 2915

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1722  ax-4 1737  ax-5 1839  ax-6 1888  ax-7 1935  ax-12 2047

This theorem depends on definitions:  df-bi 197  df-an 386  df-tru 1486  df-ex 1705  df-nf 1710  df-eu 2474  df-mo 2475  df-rmo 2920

This theorem is referenced by:  reuxfr2d  4891  brdom7disj  9353  reuxfr3d  29329  cvmlift2lem13  31297  nomaxmo  31847  ineccnvmo  34122  2reu5a  41177