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Theorem bj-ax6elem1 36634
Description: Lemma for bj-ax6e 36636. (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 2390 . 2 (¬ ∀𝑥 𝑥 = 𝑦 → (¬ ∀𝑥 𝑥 = 𝑧 → (𝑦 = 𝑧 → ∀𝑥 𝑦 = 𝑧)))
2 axc16 2262 . 2 (∀𝑥 𝑥 = 𝑧 → (𝑦 = 𝑧 → ∀𝑥 𝑦 = 𝑧))
31, 2pm2.61d2 181 1 (¬ ∀𝑥 𝑥 = 𝑦 → (𝑦 = 𝑧 → ∀𝑥 𝑦 = 𝑧))
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wi 4  wal 1535
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1793  ax-4 1807  ax-5 1909  ax-6 1967  ax-7 2007  ax-10 2141  ax-12 2178  ax-13 2380
This theorem depends on definitions:  df-bi 207  df-an 396  df-or 847  df-tru 1540  df-ex 1778  df-nf 1782
This theorem is referenced by:  bj-ax6e  36636
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