Description: Consequence of the not-free predicate. (Contributed by Mario Carneiro, 11-Aug-2016) Avoid ax-10 , ax-11 . (Revised by GG, 23-May-2024)
Ref | Expression | ||
---|---|---|---|
Hypothesis | nfcrii.1 | ⊢ Ⅎ 𝑥 𝐴 | |
Assertion | nfcrii | ⊢ ( 𝑦 ∈ 𝐴 → ∀ 𝑥 𝑦 ∈ 𝐴 ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nfcrii.1 | ⊢ Ⅎ 𝑥 𝐴 | |
2 | 1 | nfcri | ⊢ Ⅎ 𝑥 𝑦 ∈ 𝐴 |
3 | 2 | nf5ri | ⊢ ( 𝑦 ∈ 𝐴 → ∀ 𝑥 𝑦 ∈ 𝐴 ) |