Metamath Proof Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > MPE Home > Th. List > nfreu1 | Structured version Visualization version GIF version |
Description: The setvar 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 2903 | . 2 ⊢ (∃!𝑥 ∈ 𝐴 𝜑 ↔ ∃!𝑥(𝑥 ∈ 𝐴 ∧ 𝜑)) | |
2 | nfeu1 2468 | . 2 ⊢ Ⅎ𝑥∃!𝑥(𝑥 ∈ 𝐴 ∧ 𝜑) | |
3 | 1, 2 | nfxfr 1771 | 1 ⊢ Ⅎ𝑥∃!𝑥 ∈ 𝐴 𝜑 |
Colors of variables: wff setvar class |
Syntax hints: ∧ wa 383 Ⅎwnf 1699 ∈ wcel 1977 ∃!weu 2458 ∃!wreu 2898 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1713 ax-4 1728 ax-5 1827 ax-6 1875 ax-7 1922 ax-10 2006 ax-11 2021 ax-12 2034 |
This theorem depends on definitions: df-bi 196 df-or 384 df-ex 1696 df-nf 1701 df-eu 2462 df-reu 2903 |
This theorem is referenced by: riota2df 6531 2reu8 39841 iccpartdisj 39975 |
Copyright terms: Public domain | W3C validator |