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Theorem hbnae-o 34735
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 2459 using ax-c11 34694. (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 34710 . 2 (∀𝑥 𝑥 = 𝑦 → ∀𝑧𝑥 𝑥 = 𝑦)
21hbn 2293 1 (¬ ∀𝑥 𝑥 = 𝑦 → ∀𝑧 ¬ ∀𝑥 𝑥 = 𝑦)
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wi 4  wal 1630
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1871  ax-4 1886  ax-5 1988  ax-6 2054  ax-7 2090  ax-10 2168  ax-11 2183  ax-12 2196  ax-c5 34690  ax-c4 34691  ax-c7 34692  ax-c10 34693  ax-c11 34694  ax-c9 34697
This theorem depends on definitions:  df-bi 197  df-or 384  df-an 385  df-ex 1854  df-nf 1859
This theorem is referenced by:  dvelimf-o  34736  ax12indalem  34752  ax12inda2ALT  34753
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