Theorem hbaev 2093

Description: All variables are effectively bound in an identical variable specifier. Version of hbae 2460 with a disjoint variable condition, requiring fewer axioms. Instance of aev2 2092. (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 2092	1 ⊢ (∀𝑥 𝑥 = 𝑦 → ∀𝑧∀𝑥 𝑥 = 𝑦)

This proof depends on syntax axioms:   → wi 4  ∀wal 1567

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1827  ax-4 1841  ax-5 1942  ax-6 1999  ax-7 2040

This proof depends on definitions:  df-bi 210  df-an 402  df-ex 1812

This theorem is used by:  dral1v  2398  euae  2684  wl-moae  38541