Theorem ich2al 47341

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 2152	. 2 ⊢ Ⅎ𝑥∀𝑥∀𝑦𝜑
2		nfa2 2177	. 2 ⊢ Ⅎ𝑦∀𝑥∀𝑦𝜑
3	1, 2	ichf 47324	1 ⊢ [𝑥⇄𝑦]∀𝑥∀𝑦𝜑

Syntax hints:  ∀wal 1535  [wich 47319

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  ax-10 2141  ax-11 2158  ax-12 2178

This theorem depends on definitions:  df-bi 207  df-or 847  df-ex 1778  df-nf 1782  df-sb 2065  df-ich 47320

This theorem is referenced by: (None)