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Theorem hba1 1786
 Description: x is not free in ∀xφ. Example in Appendix in [Megill] p. 450 (p. 19 of the preprint). Also Lemma 22 of [Monk2] p. 114. (Contributed by NM, 5-Aug-1993.) (Proof shortened by Wolf Lammen, 15-Dec-2017.)
Assertion
Ref Expression
hba1 (xφxxφ)

Proof of Theorem hba1
StepHypRef Expression
1 hbe1 1731 . . 3 (x ¬ φxx ¬ φ)
21hbn 1776 . 2 x ¬ φx ¬ x ¬ φ)
3 alex 1572 . 2 (xφ ↔ ¬ x ¬ φ)
43albii 1566 . 2 (xxφx ¬ x ¬ φ)
52, 3, 43imtr4i 257 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-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-11 1746 This theorem depends on definitions:  df-bi 177  df-ex 1542 This theorem is referenced by:  nfa1  1788  spimehOLD  1821  19.21hOLD  1840  19.12OLD  1848  cbv3hvOLD  1851  nfald  1852  ax12olem5  1931  ax10lem4  1941  ax9  1949  dvelimh  1964  axi5r  2326  axial  2327  hbra1  2663
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