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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 3147 | . 2 ⊢ (∃!𝑥 ∈ 𝐴 𝜑 ↔ ∃!𝑥(𝑥 ∈ 𝐴 ∧ 𝜑)) | |
2 | nfeu1 2674 | . 2 ⊢ Ⅎ𝑥∃!𝑥(𝑥 ∈ 𝐴 ∧ 𝜑) | |
3 | 1, 2 | nfxfr 1853 | 1 ⊢ Ⅎ𝑥∃!𝑥 ∈ 𝐴 𝜑 |
Colors of variables: wff setvar class |
Syntax hints: ∧ wa 398 Ⅎwnf 1784 ∈ wcel 2114 ∃!weu 2653 ∃!wreu 3142 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1796 ax-4 1810 ax-5 1911 ax-6 1970 ax-7 2015 ax-10 2145 ax-11 2161 ax-12 2177 |
This theorem depends on definitions: df-bi 209 df-an 399 df-or 844 df-ex 1781 df-nf 1785 df-mo 2622 df-eu 2654 df-reu 3147 |
This theorem is referenced by: riota2df 7139 2reu8 43318 iccpartdisj 43604 |
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