Theorem ich2al 48752

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 2191	. 2 ⊢ Ⅎ𝑥∀𝑥∀𝑦𝜑
2		nfa2 2213	. 2 ⊢ Ⅎ𝑦∀𝑥∀𝑦𝜑
3	1, 2	ichf 48735	1 ⊢ [𝑥⇄𝑦]∀𝑥∀𝑦𝜑

This proof depends on syntax axioms:  ∀wal 1568  [wich 48730

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1828  ax-4 1842  ax-5 1945  ax-6 2002  ax-7 2043  ax-10 2180  ax-11 2197  ax-12 2216

This proof depends on definitions:  df-bi 210  df-an 402  df-or 862  df-ex 1813  df-nf 1817  df-sb 2102  df-ich 48731

This theorem is used by: (None)