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Theorem bj-ax6elem1 32988
 Description: Lemma for bj-ax6e 32990. (Contributed by BJ, 22-Dec-2020.) (Proof modification is discouraged.)
Assertion
Ref Expression
bj-ax6elem1 (¬ ∀𝑥 𝑥 = 𝑦 → (𝑦 = 𝑧 → ∀𝑥 𝑦 = 𝑧))
Distinct variable group:   𝑥,𝑧

Proof of Theorem bj-ax6elem1
StepHypRef Expression
1 axc9 2458 . 2 (¬ ∀𝑥 𝑥 = 𝑦 → (¬ ∀𝑥 𝑥 = 𝑧 → (𝑦 = 𝑧 → ∀𝑥 𝑦 = 𝑧)))
2 axc16 2300 . 2 (∀𝑥 𝑥 = 𝑧 → (𝑦 = 𝑧 → ∀𝑥 𝑦 = 𝑧))
31, 2pm2.61d2 173 1 (¬ ∀𝑥 𝑥 = 𝑦 → (𝑦 = 𝑧 → ∀𝑥 𝑦 = 𝑧))
 Colors of variables: wff setvar class Syntax hints:  ¬ wn 3   → wi 4  ∀wal 1629 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1870  ax-4 1885  ax-5 1991  ax-6 2057  ax-7 2093  ax-10 2174  ax-12 2203  ax-13 2408 This theorem depends on definitions:  df-bi 197  df-an 383  df-or 837  df-tru 1634  df-ex 1853  df-nf 1858 This theorem is referenced by:  bj-ax6e  32990
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