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Theorem nfich2 45730
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 45728 . 2 ([𝑥𝑦]𝜑 ↔ ∀𝑥𝑦([𝑥 / 𝑎][𝑦 / 𝑥][𝑎 / 𝑦]𝜑𝜑))
2 nfa2 2171 . 2 𝑦𝑥𝑦([𝑥 / 𝑎][𝑦 / 𝑥][𝑎 / 𝑦]𝜑𝜑)
31, 2nfxfr 1856 1 𝑦[𝑥𝑦]𝜑
Colors of variables: wff setvar class
Syntax hints:  wb 205  wal 1540  wnf 1786  [wsb 2068  [wich 45727
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1798  ax-4 1812  ax-10 2138  ax-11 2155
This theorem depends on definitions:  df-bi 206  df-or 847  df-ex 1783  df-nf 1787  df-ich 45728
This theorem is referenced by:  ich2exprop  45753  ichreuopeq  45755
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