Theorem hbaev 1972

Description: Version of hbae 2303 with a DV condition, requiring fewer axioms. Instance of hbaevg 1971 and aev2 1973. (Contributed by Wolf Lammen, 22-Mar-2021.)

Assertion

Ref	Expression
hbaev	⊢ (∀𝑥 𝑥 = 𝑦 → ∀𝑧∀𝑥 𝑥 = 𝑦)

Distinct variable group:   𝑥,𝑦

Proof of Theorem hbaev

Step	Hyp	Ref	Expression
1		hbaevg 1971	1 ⊢ (∀𝑥 𝑥 = 𝑦 → ∀𝑧∀𝑥 𝑥 = 𝑦)

Syntax hints:   → 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

This theorem depends on definitions:  df-bi 196  df-an 385  df-ex 1696

This theorem is referenced by: (None)