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Mirrors > Home > ILE Home > Th. List > nfcii | GIF version |
Description: Deduce that a class 𝐴 does not have 𝑥 free in it. (Contributed by Mario Carneiro, 11-Aug-2016.) |
Ref | Expression |
---|---|
nfcii.1 | ⊢ (𝑦 ∈ 𝐴 → ∀𝑥 𝑦 ∈ 𝐴) |
Ref | Expression |
---|---|
nfcii | ⊢ Ⅎ𝑥𝐴 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nfcii.1 | . . 3 ⊢ (𝑦 ∈ 𝐴 → ∀𝑥 𝑦 ∈ 𝐴) | |
2 | 1 | nfi 1391 | . 2 ⊢ Ⅎ𝑥 𝑦 ∈ 𝐴 |
3 | 2 | nfci 2209 | 1 ⊢ Ⅎ𝑥𝐴 |
Colors of variables: wff set class |
Syntax hints: → wi 4 ∀wal 1282 ∈ wcel 1433 Ⅎwnfc 2206 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 104 ax-ia2 105 ax-ia3 106 ax-gen 1378 |
This theorem depends on definitions: df-bi 115 df-nf 1390 df-nfc 2208 |
This theorem is referenced by: (None) |
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