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Theorem alexn 1579
Description: A relationship between two quantifiers and negation. (Contributed by NM, 18-Aug-1993.)
Assertion
Ref Expression
alexn (xy ¬ φ ↔ ¬ xyφ)

Proof of Theorem alexn
StepHypRef Expression
1 exnal 1574 . . 3 (y ¬ φ ↔ ¬ yφ)
21albii 1566 . 2 (xy ¬ φx ¬ yφ)
3 alnex 1543 . 2 (x ¬ yφ ↔ ¬ xyφ)
42, 3bitri 240 1 (xy ¬ φ ↔ ¬ xyφ)
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wb 176  wal 1540  wex 1541
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1546  ax-5 1557
This theorem depends on definitions:  df-bi 177  df-ex 1542
This theorem is referenced by:  2exnexn  1580
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