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Mirrors > Home > ILE Home > Th. List > nfcrd | GIF version |
Description: Consequence of the not-free predicate. (Contributed by Mario Carneiro, 11-Aug-2016.) |
Ref | Expression |
---|---|
nfeqd.1 | ⊢ (𝜑 → Ⅎ𝑥𝐴) |
Ref | Expression |
---|---|
nfcrd | ⊢ (𝜑 → Ⅎ𝑥 𝑦 ∈ 𝐴) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nfeqd.1 | . 2 ⊢ (𝜑 → Ⅎ𝑥𝐴) | |
2 | nfcr 2298 | . 2 ⊢ (Ⅎ𝑥𝐴 → Ⅎ𝑥 𝑦 ∈ 𝐴) | |
3 | 1, 2 | syl 14 | 1 ⊢ (𝜑 → Ⅎ𝑥 𝑦 ∈ 𝐴) |
Colors of variables: wff set class |
Syntax hints: → wi 4 Ⅎwnf 1447 ∈ wcel 2135 Ⅎwnfc 2293 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 105 ax-4 1497 |
This theorem depends on definitions: df-bi 116 df-nfc 2295 |
This theorem is referenced by: nfeqd 2321 nfeld 2322 dvelimdc 2327 nfcsbd 3075 nfcsbw 3076 nfifd 3542 |
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