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Theorem nfich2 44008
 Description: The second interchangeable setvar variable is not free. (Contributed by AV, 21-Aug-2023.)
Assertion
Ref Expression
nfich2 𝑦[𝑥𝑦]𝜑

Proof of Theorem nfich2
Dummy variable 𝑎 is distinct from all other variables.
StepHypRef Expression
1 df-ich 44006 . 2 ([𝑥𝑦]𝜑 ↔ ∀𝑥𝑦([𝑥 / 𝑎][𝑦 / 𝑥][𝑎 / 𝑦]𝜑𝜑))
2 nfa2 2174 . 2 𝑦𝑥𝑦([𝑥 / 𝑎][𝑦 / 𝑥][𝑎 / 𝑦]𝜑𝜑)
31, 2nfxfr 1854 1 𝑦[𝑥𝑦]𝜑
 Colors of variables: wff setvar class Syntax hints:   ↔ wb 209  ∀wal 1536  Ⅎwnf 1785  [wsb 2069  [wich 44005 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-10 2142  ax-11 2158 This theorem depends on definitions:  df-bi 210  df-or 845  df-ex 1782  df-nf 1786  df-ich 44006 This theorem is referenced by:  ich2exprop  44031  ichreuopeq  44033
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