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Theorem aaan 1884
 Description: Rearrange universal quantifiers. (Contributed by NM, 12-Aug-1993.)
Hypotheses
Ref Expression
aaan.1 yφ
aaan.2 xψ
Assertion
Ref Expression
aaan (xy(φ ψ) ↔ (xφ yψ))

Proof of Theorem aaan
StepHypRef Expression
1 aaan.1 . . . 4 yφ
2119.28 1870 . . 3 (y(φ ψ) ↔ (φ yψ))
32albii 1566 . 2 (xy(φ ψ) ↔ x(φ yψ))
4 aaan.2 . . . 4 xψ
54nfal 1842 . . 3 xyψ
6519.27 1869 . 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   ∧ wa 358  ∀wal 1540  Ⅎwnf 1544 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  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:  mo  2226  2mo  2282  2eu4  2287
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