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Theorem hbnaes 2419
Description: Rule that applies hbnae 2417 to antecedent. (Contributed by NM, 15-May-1993.)
Hypothesis
Ref Expression
hbnaes.1 (∀𝑧 ¬ ∀𝑥 𝑥 = 𝑦𝜑)
Assertion
Ref Expression
hbnaes (¬ ∀𝑥 𝑥 = 𝑦𝜑)

Proof of Theorem hbnaes
StepHypRef Expression
1 hbnae 2417 . 2 (¬ ∀𝑥 𝑥 = 𝑦 → ∀𝑧 ¬ ∀𝑥 𝑥 = 𝑦)
2 hbnaes.1 . 2 (∀𝑧 ¬ ∀𝑥 𝑥 = 𝑦𝜑)
31, 2syl 17 1 (¬ ∀𝑥 𝑥 = 𝑦𝜑)
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wi 4  wal 1651
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1891  ax-4 1905  ax-5 2006  ax-6 2072  ax-7 2107  ax-10 2185  ax-11 2200  ax-12 2213  ax-13 2354
This theorem depends on definitions:  df-bi 199  df-an 386  df-or 875  df-tru 1657  df-ex 1876  df-nf 1880
This theorem is referenced by: (None)
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