Theorem hbaev 2064

Description: All variables are effectively bound in an identical variable specifier. Version of hbae 2442 with a disjoint variable condition, requiring fewer axioms. Instance of aev2 2063. (Contributed by NM, 13-May-1993.) (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 2063	1 ⊢ (∀𝑥 𝑥 = 𝑦 → ∀𝑧∀𝑥 𝑥 = 𝑦)

Syntax hints:   → wi 4  ∀wal 1536

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1797  ax-4 1811  ax-5 1911  ax-6 1970  ax-7 2015

This theorem depends on definitions:  df-bi 210  df-an 400  df-ex 1782

This theorem is referenced by:  nfnaew  2150  euae  2681  wl-moae  35223