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Mirrors > Home > ILE Home > Th. List > nfci | GIF version |
Description: Deduce that a class 𝐴 does not have 𝑥 free in it. (Contributed by Mario Carneiro, 11-Aug-2016.) |
Ref | Expression |
---|---|
nfci.1 | ⊢ Ⅎ𝑥 𝑦 ∈ 𝐴 |
Ref | Expression |
---|---|
nfci | ⊢ Ⅎ𝑥𝐴 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-nfc 2167 | . 2 ⊢ (Ⅎ𝑥𝐴 ↔ ∀𝑦Ⅎ𝑥 𝑦 ∈ 𝐴) | |
2 | nfci.1 | . 2 ⊢ Ⅎ𝑥 𝑦 ∈ 𝐴 | |
3 | 1, 2 | mpgbir 1342 | 1 ⊢ Ⅎ𝑥𝐴 |
Colors of variables: wff set class |
Syntax hints: Ⅎwnf 1349 ∈ wcel 1393 Ⅎwnfc 2165 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 99 ax-ia2 100 ax-ia3 101 ax-gen 1338 |
This theorem depends on definitions: df-bi 110 df-nfc 2167 |
This theorem is referenced by: nfcii 2169 nfcv 2178 nfab1 2180 nfab 2182 |
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