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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 2270 | . 2 ⊢ (Ⅎ𝑥𝐴 ↔ ∀𝑦Ⅎ𝑥 𝑦 ∈ 𝐴) | |
2 | nfnf1 1523 | . . 3 ⊢ Ⅎ𝑥Ⅎ𝑥 𝑦 ∈ 𝐴 | |
3 | 2 | nfal 1555 | . 2 ⊢ Ⅎ𝑥∀𝑦Ⅎ𝑥 𝑦 ∈ 𝐴 |
4 | 1, 3 | nfxfr 1450 | 1 ⊢ Ⅎ𝑥Ⅎ𝑥𝐴 |
Colors of variables: wff set class |
Syntax hints: ∀wal 1329 Ⅎwnf 1436 ∈ wcel 1480 Ⅎwnfc 2268 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-5 1423 ax-7 1424 ax-gen 1425 ax-4 1487 ax-ial 1514 |
This theorem depends on definitions: df-bi 116 df-nf 1437 df-nfc 2270 |
This theorem is referenced by: vtoclgft 2736 sbcralt 2985 sbcrext 2986 csbiebt 3039 nfopd 3722 nfimad 4890 nffvd 5433 |
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