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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 2919 | . 2 ⊢ (∃!𝑥 ∈ 𝐴 𝜑 ↔ ∃!𝑥(𝑥 ∈ 𝐴 ∧ 𝜑)) | |
2 | nfeu1 2480 | . 2 ⊢ Ⅎ𝑥∃!𝑥(𝑥 ∈ 𝐴 ∧ 𝜑) | |
3 | 1, 2 | nfxfr 1779 | 1 ⊢ Ⅎ𝑥∃!𝑥 ∈ 𝐴 𝜑 |
Colors of variables: wff setvar class |
Syntax hints: ∧ wa 384 Ⅎwnf 1708 ∈ wcel 1990 ∃!weu 2470 ∃!wreu 2914 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1722 ax-4 1737 ax-5 1839 ax-6 1888 ax-7 1935 ax-10 2019 ax-11 2034 ax-12 2047 |
This theorem depends on definitions: df-bi 197 df-or 385 df-ex 1705 df-nf 1710 df-eu 2474 df-reu 2919 |
This theorem is referenced by: riota2df 6631 2reu8 41192 iccpartdisj 41373 |
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