Theorem reubii 1785

Description: Formula-building rule for restricted existential quantifier (inference rule).

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 8	. 2 |- (x e. A -> (ph <-> ps))
3	2	reubiia 1784	1 |- (E!x e. A ph <-> E!x e. A ps)

Syntax hints:   <-> wb 146   e. wcel 960  E!wreu 1650

This theorem is referenced by:  aceq2 4741  infmsup 6070  uzwo3 6220  cnlnadjlem3 9997  cnlnadjlem4 9998  cnlnadjlem5 9999

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-gen 965  ax-12 970  ax-17 973  ax-4 975  ax-5o 977  ax-6o 980  ax-9o 1125

This theorem depends on definitions:  df-bi 147  df-an 225  df-ex 983  df-eu 1384  df-reu 1654

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