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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 2325 | . 2 ⊢ (Ⅎ𝑥𝐴 ↔ ∀𝑦Ⅎ𝑥 𝑦 ∈ 𝐴) | |
2 | nfnf1 1555 | . . 3 ⊢ Ⅎ𝑥Ⅎ𝑥 𝑦 ∈ 𝐴 | |
3 | 2 | nfal 1587 | . 2 ⊢ Ⅎ𝑥∀𝑦Ⅎ𝑥 𝑦 ∈ 𝐴 |
4 | 1, 3 | nfxfr 1485 | 1 ⊢ Ⅎ𝑥Ⅎ𝑥𝐴 |
Colors of variables: wff set class |
Syntax hints: ∀wal 1362 Ⅎwnf 1471 ∈ wcel 2164 Ⅎwnfc 2323 |
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 1458 ax-7 1459 ax-gen 1460 ax-ial 1545 |
This theorem depends on definitions: df-bi 117 df-nf 1472 df-nfc 2325 |
This theorem is referenced by: vtoclgft 2810 sbcralt 3062 sbcrext 3063 csbiebt 3120 nfopd 3821 nfimad 5014 nffvd 5566 |
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