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Theorem eeor 1885
 Description: Rearrange existential quantifiers. (Contributed by NM, 8-Aug-1994.)
Hypotheses
Ref Expression
eeor.1 yφ
eeor.2 xψ
Assertion
Ref Expression
eeor (xy(φ ψ) ↔ (xφ yψ))

Proof of Theorem eeor
StepHypRef Expression
1 eeor.1 . . . 4 yφ
2119.45 1878 . . 3 (y(φ ψ) ↔ (φ yψ))
32exbii 1582 . 2 (xy(φ ψ) ↔ x(φ yψ))
4 eeor.2 . . . 4 xψ
54nfex 1843 . . 3 xyψ
6519.44 1877 . 2 (x(φ yψ) ↔ (xφ yψ))
73, 6bitri 240 1 (xy(φ ψ) ↔ (xφ yψ))
 Colors of variables: wff setvar class Syntax hints:   ↔ wb 176   ∨ wo 357  ∃wex 1541  Ⅎwnf 1544 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-7 1734  ax-11 1746 This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-ex 1542  df-nf 1545 This theorem is referenced by: (None)
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