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Theorem hbe1 1731
Description: x is not free in xφ. (Contributed by NM, 5-Aug-1993.)
Assertion
Ref Expression
hbe1 (xφxxφ)

Proof of Theorem hbe1
StepHypRef Expression
1 df-ex 1542 . 2 (xφ ↔ ¬ x ¬ φ)
2 hbn1 1730 . 2 x ¬ φx ¬ x ¬ φ)
31, 2hbxfrbi 1568 1 (xφxxφ)
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wi 4  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  ax-6 1729
This theorem depends on definitions:  df-bi 177  df-ex 1542
This theorem is referenced by:  nfe1  1732  hba1  1786  19.23hOLD  1820  ax12olem5  1931  ax10lem2  1937  axie1  2328  hboprab1  5559  hboprab2  5560  hboprab3  5561
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