Theorem reubii 2555

Description: Formula-building rule for restricted existential quantifier (inference form). (Contributed by NM, 22-Oct-1999.)

Hypothesis

Ref	Expression
reubii.1	|- ( ph <-> ps )

Assertion

Ref	Expression
reubii	|- ( E! x e. A ph <-> E! x e. A ps )

Proof of Theorem reubii

Step	Hyp	Ref	Expression
1		reubii.1	. . 3 |- ( ph <-> ps )
2	1	a1i 9	. 2 |- ( x e. A -> ( ph <-> ps ) )
3	2	reubiia 2554	1 |- ( E! x e. A ph <-> E! x e. A ps )

Syntax hints:   <-> wb 104   e. wcel 1439   E!wreu 2362

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-5 1382  ax-gen 1384  ax-ie1 1428  ax-ie2 1429  ax-4 1446  ax-17 1465  ax-ial 1473

This theorem depends on definitions:  df-bi 116  df-tru 1293  df-nf 1396  df-eu 1952  df-reu 2367

This theorem is referenced by:  caucvgsrlemcl  7397  axcaucvglemcl  7493  axcaucvglemval  7495