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Mirrors > Home > ILE Home > Th. List > nfreu1 | GIF version |
Description: 𝑥 is not free in ∃!𝑥 ∈ 𝐴𝜑. (Contributed by NM, 19-Mar-1997.) |
Ref | Expression |
---|---|
nfreu1 | ⊢ Ⅎ𝑥∃!𝑥 ∈ 𝐴 𝜑 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-reu 2475 | . 2 ⊢ (∃!𝑥 ∈ 𝐴 𝜑 ↔ ∃!𝑥(𝑥 ∈ 𝐴 ∧ 𝜑)) | |
2 | nfeu1 2049 | . 2 ⊢ Ⅎ𝑥∃!𝑥(𝑥 ∈ 𝐴 ∧ 𝜑) | |
3 | 1, 2 | nfxfr 1485 | 1 ⊢ Ⅎ𝑥∃!𝑥 ∈ 𝐴 𝜑 |
Colors of variables: wff set class |
Syntax hints: ∧ wa 104 Ⅎwnf 1471 ∃!weu 2038 ∈ wcel 2160 ∃!wreu 2470 |
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-ie1 1504 ax-ie2 1505 ax-4 1521 ax-ial 1545 |
This theorem depends on definitions: df-bi 117 df-nf 1472 df-eu 2041 df-reu 2475 |
This theorem is referenced by: riota2df 5873 |
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