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Theorem axc15OLD 2332
 Description: Obsolete proof of axc15 2291 as of 24-Mar-2021. (Contributed by NM, 3-Feb-2007.) (Proof modification is discouraged.) (New usage is discouraged.)
Assertion
Ref Expression
axc15OLD (¬ ∀𝑥 𝑥 = 𝑦 → (𝑥 = 𝑦 → (𝜑 → ∀𝑥(𝑥 = 𝑦𝜑))))

Proof of Theorem axc15OLD
Dummy variable 𝑧 is distinct from all other variables.
StepHypRef Expression
1 ax-12 2034 . 2 (𝑥 = 𝑧 → (∀𝑧𝜑 → ∀𝑥(𝑥 = 𝑧𝜑)))
21ax12a2OLD 2331 1 (¬ ∀𝑥 𝑥 = 𝑦 → (𝑥 = 𝑦 → (𝜑 → ∀𝑥(𝑥 = 𝑦𝜑))))
 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-12 2034  ax-13 2234 This theorem depends on definitions:  df-bi 196  df-or 384  df-an 385  df-tru 1478  df-ex 1696  df-nf 1701 This theorem is referenced by: (None)
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