Metamath Proof Explorer
Description: The first interchangeable setvar variable is not free. (Contributed by AV, 21-Aug-2023)
|
|
Ref |
Expression |
|
Assertion |
nfich1 |
⊢ Ⅎ 𝑥 [ 𝑥 ⇄ 𝑦 ] 𝜑 |
Proof
Step |
Hyp |
Ref |
Expression |
1 |
|
df-ich |
⊢ ( [ 𝑥 ⇄ 𝑦 ] 𝜑 ↔ ∀ 𝑥 ∀ 𝑦 ( [ 𝑥 / 𝑎 ] [ 𝑦 / 𝑥 ] [ 𝑎 / 𝑦 ] 𝜑 ↔ 𝜑 ) ) |
2 |
|
nfa1 |
⊢ Ⅎ 𝑥 ∀ 𝑥 ∀ 𝑦 ( [ 𝑥 / 𝑎 ] [ 𝑦 / 𝑥 ] [ 𝑎 / 𝑦 ] 𝜑 ↔ 𝜑 ) |
3 |
1 2
|
nfxfr |
⊢ Ⅎ 𝑥 [ 𝑥 ⇄ 𝑦 ] 𝜑 |