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Theorem hbaev 2055
Description: Version of hbae 2445 with a disjoint variable condition, requiring fewer axioms. Instance of aev2 2054. (Contributed by Wolf Lammen, 22-Mar-2021.)
Assertion
Ref Expression
hbaev (∀𝑥 𝑥 = 𝑦 → ∀𝑧𝑥 𝑥 = 𝑦)
Distinct variable group:   𝑥,𝑦

Proof of Theorem hbaev
StepHypRef Expression
1 aev2 2054 1 (∀𝑥 𝑥 = 𝑦 → ∀𝑧𝑥 𝑥 = 𝑦)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wal 1526
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1787  ax-4 1801  ax-5 1902  ax-6 1961  ax-7 2006
This theorem depends on definitions:  df-bi 208  df-an 397  df-ex 1772
This theorem is referenced by:  nfnaew  2144  euae  2740  wl-moae  34638
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