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Theorem hbnae 2437
Description: All variables are effectively bound in a distinct variable specifier. Lemma L19 in [Megill] p. 446 (p. 14 of the preprint). Usage of this theorem is discouraged because it depends on ax-13 2377. Use the weaker hbnaev 2062 when possible. (Contributed by NM, 13-May-1993.) (New usage is discouraged.)
Assertion
Ref Expression
hbnae (¬ ∀𝑥 𝑥 = 𝑦 → ∀𝑧 ¬ ∀𝑥 𝑥 = 𝑦)

Proof of Theorem hbnae
StepHypRef Expression
1 hbae 2436 . 2 (∀𝑥 𝑥 = 𝑦 → ∀𝑧𝑥 𝑥 = 𝑦)
21hbn 2295 1 (¬ ∀𝑥 𝑥 = 𝑦 → ∀𝑧 ¬ ∀𝑥 𝑥 = 𝑦)
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wi 4  wal 1538
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1795  ax-4 1809  ax-5 1910  ax-6 1967  ax-7 2007  ax-10 2141  ax-11 2157  ax-12 2177  ax-13 2377
This theorem depends on definitions:  df-bi 207  df-an 396  df-or 849  df-tru 1543  df-ex 1780  df-nf 1784
This theorem is referenced by:  hbnaes  2440  eujustALT  2572  bj-hbnaeb  36821  ax6e2nd  44578  ax6e2ndVD  44928  ax6e2ndeqVD  44929  ax6e2ndALT  44950  ax6e2ndeqALT  44951
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