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Theorem ich2al 47454
Description: Two setvar variables are always interchangeable when there are two universal quantifiers. (Contributed by SN, 23-Nov-2023.)
Assertion
Ref Expression
ich2al [𝑥𝑦]∀𝑥𝑦𝜑

Proof of Theorem ich2al
StepHypRef Expression
1 nfa1 2151 . 2 𝑥𝑥𝑦𝜑
2 nfa2 2176 . 2 𝑦𝑥𝑦𝜑
31, 2ichf 47437 1 [𝑥𝑦]∀𝑥𝑦𝜑
Colors of variables: wff setvar class
Syntax hints:  wal 1538  [wich 47432
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1795  ax-4 1809  ax-5 1910  ax-6 1967  ax-7 2007  ax-10 2141  ax-11 2157  ax-12 2177
This theorem depends on definitions:  df-bi 207  df-or 849  df-ex 1780  df-nf 1784  df-sb 2065  df-ich 47433
This theorem is referenced by: (None)
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