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Theorem wl-hbae1 33433
Description: This specialization of hbae 2348 does not depend on ax-11 2074. (Contributed by Wolf Lammen, 8-Aug-2021.)
Assertion
Ref Expression
wl-hbae1 (∀𝑥 𝑥 = 𝑦 → ∀𝑦𝑥 𝑥 = 𝑦)

Proof of Theorem wl-hbae1
StepHypRef Expression
1 axc11n 2342 . 2 (∀𝑥 𝑥 = 𝑦 → ∀𝑦 𝑦 = 𝑥)
2 axc11n 2342 . . 3 (∀𝑦 𝑦 = 𝑥 → ∀𝑥 𝑥 = 𝑦)
32axc4i 2169 . 2 (∀𝑦 𝑦 = 𝑥 → ∀𝑦𝑥 𝑥 = 𝑦)
41, 3syl 17 1 (∀𝑥 𝑥 = 𝑦 → ∀𝑦𝑥 𝑥 = 𝑦)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wal 1521
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1762  ax-4 1777  ax-5 1879  ax-6 1945  ax-7 1981  ax-10 2059  ax-12 2087  ax-13 2282
This theorem depends on definitions:  df-bi 197  df-or 384  df-an 385  df-ex 1745  df-nf 1750
This theorem is referenced by: (None)
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