Theorem hbaev 2080

Description: All variables are effectively bound in an identical variable specifier. Version of hbae 2461 with a disjoint variable condition, requiring fewer axioms. Instance of aev2 2079. (Contributed by NM, 13-May-1993.) Reduce axiom usage. (Revised 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		aev2 2079	1 ⊢ (∀𝑥 𝑥 = 𝑦 → ∀𝑧∀𝑥 𝑥 = 𝑦)

Syntax hints:   → wi 4  ∀wal 1557

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1814  ax-4 1828  ax-5 1929  ax-6 1986  ax-7 2027

This theorem depends on definitions:  df-bi 209  df-an 400  df-ex 1799

This theorem is referenced by:  dral1v  2399  euae  2685  wl-moae  37983