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| Mirrors > Home > ILE Home > Th. List > nfnfc1 | GIF version | ||
| Description: 𝑥 is bound in Ⅎ𝑥𝐴. (Contributed by Mario Carneiro, 11-Aug-2016.) |
| Ref | Expression |
|---|---|
| nfnfc1 | ⊢ Ⅎ𝑥Ⅎ𝑥𝐴 |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | df-nfc 2328 | . 2 ⊢ (Ⅎ𝑥𝐴 ↔ ∀𝑦Ⅎ𝑥 𝑦 ∈ 𝐴) | |
| 2 | nfnf1 1558 | . . 3 ⊢ Ⅎ𝑥Ⅎ𝑥 𝑦 ∈ 𝐴 | |
| 3 | 2 | nfal 1590 | . 2 ⊢ Ⅎ𝑥∀𝑦Ⅎ𝑥 𝑦 ∈ 𝐴 |
| 4 | 1, 3 | nfxfr 1488 | 1 ⊢ Ⅎ𝑥Ⅎ𝑥𝐴 |
| Colors of variables: wff set class |
| Syntax hints: ∀wal 1362 Ⅎwnf 1474 ∈ wcel 2167 Ⅎwnfc 2326 |
| This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 106 ax-ia2 107 ax-ia3 108 ax-5 1461 ax-7 1462 ax-gen 1463 ax-ial 1548 |
| This theorem depends on definitions: df-bi 117 df-nf 1475 df-nfc 2328 |
| This theorem is referenced by: vtoclgft 2814 sbcralt 3066 sbcrext 3067 csbiebt 3124 nfopd 3825 nfimad 5018 nffvd 5570 |
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