Theorem reubii 1782

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 1781	1 |- (E!x e. A ph <-> E!x e. A ps)

Syntax hints:   <-> wb 146   e. wcel 958  E!wreu 1647

This theorem is referenced by:  aceq2 4731  infmsup 6068  uzwo3 6218  cnlnadjlem3 10002  cnlnadjlem4 10003  cnlnadjlem5 10004

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-gen 963  ax-12 968  ax-17 971  ax-4 973  ax-5o 975  ax-6o 978  ax-9o 1123

This theorem depends on definitions:  df-bi 147  df-an 225  df-ex 981  df-eu 1382  df-reu 1651

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