Theorem ich2al 48549

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 2187	. 2 ⊢ Ⅎ𝑥∀𝑥∀𝑦𝜑
2		nfa2 2209	. 2 ⊢ Ⅎ𝑦∀𝑥∀𝑦𝜑
3	1, 2	ichf 48532	1 ⊢ [𝑥⇄𝑦]∀𝑥∀𝑦𝜑

This proof depends on syntax axioms:  ∀wal 1567  [wich 48527

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  ax-10 2177  ax-11 2193  ax-12 2212

This proof depends on definitions:  df-bi 210  df-an 402  df-or 862  df-ex 1812  df-nf 1816  df-sb 2099  df-ich 48528

This theorem is used by: (None)