Theorem ich2al 47942

Description: Two setvar variables are always interchangeable when there are two universal quantifiers. (Contributed by SN, 23-Nov-2023.)

Assertion

Ref	Expression
ich2al	⊢ [𝑥⇄𝑦]∀𝑥∀𝑦𝜑

Proof of Theorem ich2al

Step	Hyp	Ref	Expression
1		nfa1 2162	. 2 ⊢ Ⅎ𝑥∀𝑥∀𝑦𝜑
2		nfa2 2186	. 2 ⊢ Ⅎ𝑦∀𝑥∀𝑦𝜑
3	1, 2	ichf 47925	1 ⊢ [𝑥⇄𝑦]∀𝑥∀𝑦𝜑

Syntax hints:  ∀wal 1545  [wich 47920

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1802  ax-4 1816  ax-5 1917  ax-6 1974  ax-7 2015  ax-10 2152  ax-11 2168  ax-12 2189

This theorem depends on definitions:  df-bi 208  df-an 397  df-or 854  df-ex 1787  df-nf 1791  df-sb 2074  df-ich 47921

This theorem is referenced by: (None)