Theorem reubii 2721

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 2720	1 |- ( E! x e. A ph <-> E! x e. A ps )

Syntax hints:   <-> wb 105   e. wcel 2202   E!wreu 2513

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-5 1496  ax-gen 1498  ax-ie1 1542  ax-ie2 1543  ax-4 1559  ax-17 1575  ax-ial 1583

This theorem depends on definitions:  df-bi 117  df-tru 1401  df-nf 1510  df-eu 2082  df-reu 2518

This theorem is referenced by:  caucvgsrlemcl  8069  axcaucvglemcl  8175  axcaucvglemval  8177  uspgredgiedg  16119  uspgriedgedg  16120  usgredg2vlem1  16163  usgredg2vlem2  16164