Theorem nfich2 48059

Description: The second interchangeable setvar variable is not free. (Contributed by AV, 21-Aug-2023.)

Assertion

Ref	Expression
nfich2	⊢ Ⅎ𝑦[𝑥⇄𝑦]𝜑

Proof of Theorem nfich2

Dummy variable 𝑎 is distinct from all other variables.

Step	Hyp	Ref	Expression
1		df-ich 48057	. 2 ⊢ ([𝑥⇄𝑦]𝜑 ↔ ∀𝑥∀𝑦([𝑥 / 𝑎][𝑦 / 𝑥][𝑎 / 𝑦]𝜑 ↔ 𝜑))
2		nfa2 2211	. 2 ⊢ Ⅎ𝑦∀𝑥∀𝑦([𝑥 / 𝑎][𝑦 / 𝑥][𝑎 / 𝑦]𝜑 ↔ 𝜑)
3	1, 2	nfxfr 1875	1 ⊢ Ⅎ𝑦[𝑥⇄𝑦]𝜑

Syntax hints:   ↔ wb 208  ∀wal 1560  Ⅎwnf 1805  [wsb 2092  [wich 48056

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1817  ax-4 1831  ax-10 2177  ax-11 2193

This theorem depends on definitions:  df-bi 209  df-or 859  df-ex 1802  df-nf 1806  df-ich 48057

This theorem is referenced by:  ich2exprop  48082  ichreuopeq  48084