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Theorem aaan 1476
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 1452 . . 3 (y(φ ψ) ↔ (φ yψ))
32albii 1356 . 2 (xy(φ ψ) ↔ x(φ yψ))
4 aaan.2 . . . 4 xψ
54nfal 1465 . . 3 xyψ
6519.27 1450 . 2 (x(φ yψ) ↔ (xφ yψ))
73, 6bitri 173 1 (xy(φ ψ) ↔ (xφ yψ))
Colors of variables: wff set class
Syntax hints:   wa 97  wb 98  wal 1240  wnf 1346
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-5 1333  ax-7 1334  ax-gen 1335  ax-4 1397
This theorem depends on definitions:  df-bi 110  df-nf 1347
This theorem is referenced by: (None)
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