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Theorem hba1-o 2149
 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.) (New usage is discouraged.)
Assertion
Ref Expression
hba1-o (xφxxφ)

Proof of Theorem hba1-o
StepHypRef Expression
1 ax-4 2135 . . 3 (x ¬ xφ → ¬ xφ)
21con2i 112 . 2 (xφ → ¬ x ¬ xφ)
3 ax6 2147 . 2 x ¬ xφx ¬ x ¬ xφ)
4 ax6 2147 . . . 4 xφx ¬ xφ)
54con1i 121 . . 3 x ¬ xφxφ)
65alimi 1559 . 2 (x ¬ x ¬ xφxxφ)
72, 3, 63syl 18 1 (xφxxφ)
 Colors of variables: wff setvar class Syntax hints:  ¬ wn 3   → wi 4  ∀wal 1540 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-4 2135  ax-5o 2136  ax-6o 2137 This theorem is referenced by:  a5i-o  2150  nfa1-o  2166  ax67to6  2167  ax467to6  2171  dvelimf-o  2180  ax11indalem  2197  ax11inda2ALT  2198  ax11inda  2200
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