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Theorem ich2al 43618
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 2148 . 2 𝑥𝑥𝑦𝜑
2 nfa2 2168 . 2 𝑦𝑥𝑦𝜑
31, 2ichf 43600 1 [𝑥𝑦]∀𝑥𝑦𝜑
Colors of variables: wff setvar class
Syntax hints:  wal 1528  [wich 43595
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1789  ax-4 1803  ax-5 1904  ax-6 1963  ax-7 2008  ax-10 2138  ax-11 2153  ax-12 2169
This theorem depends on definitions:  df-bi 209  df-or 844  df-ex 1774  df-nf 1778  df-sb 2063  df-ich 43596
This theorem is referenced by: (None)
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