Theorem ich2al 43984

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 2174	. 2 ⊢ Ⅎ𝑦∀𝑥∀𝑦𝜑
3	1, 2	ichf 43967	1 ⊢ [𝑥⇄𝑦]∀𝑥∀𝑦𝜑

Syntax hints:  ∀wal 1536  [wich 43962

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1797  ax-4 1811  ax-5 1911  ax-6 1970  ax-7 2015  ax-10 2142  ax-11 2158  ax-12 2175

This theorem depends on definitions:  df-bi 210  df-or 845  df-ex 1782  df-nf 1786  df-sb 2070  df-ich 43963

This theorem is referenced by: (None)