Theorem rmobii 2500

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 9	. 2 |- ( x e. A -> ( ph <-> ps ) )
3	2	rmobiia 2499	1 |- ( E* x e. A ph <-> E* x e. A ps )

Syntax hints:   <-> wb 98   e. wcel 1393   E*wrmo 2309

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-5 1336  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-4 1400  ax-17 1419  ax-ial 1427

This theorem depends on definitions:  df-bi 110  df-tru 1246  df-nf 1350  df-eu 1903  df-mo 1904  df-rmo 2314

This theorem is referenced by: (None)