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Theorem hbnae-o 33231
 Description: All variables are effectively bound in a distinct variable specifier. Lemma L19 in [Megill] p. 446 (p. 14 of the preprint). Version of hbnae 2305 using ax-c11 33190. (Contributed by NM, 13-May-1993.) (Proof modification is discouraged.) (New usage is discouraged.)
Assertion
Ref Expression
hbnae-o (¬ ∀𝑥 𝑥 = 𝑦 → ∀𝑧 ¬ ∀𝑥 𝑥 = 𝑦)

Proof of Theorem hbnae-o
StepHypRef Expression
1 hbae-o 33206 . 2 (∀𝑥 𝑥 = 𝑦 → ∀𝑧𝑥 𝑥 = 𝑦)
21hbn 2131 1 (¬ ∀𝑥 𝑥 = 𝑦 → ∀𝑧 ¬ ∀𝑥 𝑥 = 𝑦)
 Colors of variables: wff setvar class Syntax hints:  ¬ wn 3   → wi 4  ∀wal 1473 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1713  ax-4 1728  ax-5 1827  ax-6 1875  ax-7 1922  ax-10 2006  ax-11 2021  ax-12 2034  ax-c5 33186  ax-c4 33187  ax-c7 33188  ax-c10 33189  ax-c11 33190  ax-c9 33193 This theorem depends on definitions:  df-bi 196  df-or 384  df-an 385  df-ex 1696  df-nf 1701 This theorem is referenced by:  dvelimf-o  33232  ax12indalem  33248  ax12inda2ALT  33249
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