Theorem hbaev 2059

Description: All variables are effectively bound in an identical variable specifier. Version of hbae 2439 with a disjoint variable condition, requiring fewer axioms. Instance of aev2 2058. (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 2058	1 ⊢ (∀𝑥 𝑥 = 𝑦 → ∀𝑧∀𝑥 𝑥 = 𝑦)

Syntax hints:   → wi 4  ∀wal 1535

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1793  ax-4 1807  ax-5 1909  ax-6 1967  ax-7 2007

This theorem depends on definitions:  df-bi 207  df-an 396  df-ex 1778

This theorem is referenced by:  nfnaewOLD  2150  dral1v  2375  euae  2663  wl-moae  37470