Theorem reubidv 1772

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

Hypothesis

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

Assertion

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

Distinct variable group:   ph,x

Proof of Theorem reubidv

Step	Hyp	Ref	Expression
1		reubidv.1	. . 3 |- (ph -> (ps <-> ch))
2	1	adantr 389	. 2 |- ((ph /\ x e. A) -> (ps <-> ch))
3	2	reubidva 1771	1 |- (ph -> (E!x e. A ps <-> E!x e. A ch))

Syntax hints:   -> wi 3   <-> wb 146   e. wcel 955  E!wreu 1639

This theorem is referenced by:  reueqd 1785  oawordeu 4173  aceq6b 4714  riesz4t 9912  cnlnadjlem4 9918  cnlnadjeut 9926

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-gen 960  ax-17 968  ax-4 970  ax-5o 972

This theorem depends on definitions:  df-bi 147  df-an 225  df-ex 978  df-eu 1375  df-reu 1643

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