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Theorem ee4anv 1915
 Description: Rearrange existential quantifiers. (Contributed by NM, 31-Jul-1995.)
Assertion
Ref Expression
ee4anv (xyzw(φ ψ) ↔ (xyφ zwψ))
Distinct variable groups:   φ,z   φ,w   ψ,x   ψ,y   y,z   x,w
Allowed substitution hints:   φ(x,y)   ψ(z,w)

Proof of Theorem ee4anv
StepHypRef Expression
1 excom 1741 . . 3 (yzw(φ ψ) ↔ zyw(φ ψ))
21exbii 1582 . 2 (xyzw(φ ψ) ↔ xzyw(φ ψ))
3 eeanv 1913 . . 3 (yw(φ ψ) ↔ (yφ wψ))
432exbii 1583 . 2 (xzyw(φ ψ) ↔ xz(yφ wψ))
5 eeanv 1913 . 2 (xz(yφ wψ) ↔ (xyφ zwψ))
62, 4, 53bitri 262 1 (xyzw(φ ψ) ↔ (xyφ zwψ))
 Colors of variables: wff setvar class Syntax hints:   ↔ wb 176   ∧ wa 358  ∃wex 1541 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-an 360  df-ex 1542  df-nf 1545 This theorem is referenced by:  cgsex4g  2892  funsi  5520  fntxp  5804  fnpprod  5843
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