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Mirrors > Home > MPE Home > Th. List > eueqi | Structured version Visualization version GIF version |
Description: There exists a unique set equal to a given set. Inference associated with euequ 2658. See euequ 2658 in the case of a setvar. (Contributed by NM, 5-Apr-1995.) |
Ref | Expression |
---|---|
eueqi.1 | ⊢ 𝐴 ∈ V |
Ref | Expression |
---|---|
eueqi | ⊢ ∃!𝑥 𝑥 = 𝐴 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | eueqi.1 | . 2 ⊢ 𝐴 ∈ V | |
2 | eueq 3647 | . 2 ⊢ (𝐴 ∈ V ↔ ∃!𝑥 𝑥 = 𝐴) | |
3 | 1, 2 | mpbi 233 | 1 ⊢ ∃!𝑥 𝑥 = 𝐴 |
Colors of variables: wff setvar class |
Syntax hints: = wceq 1538 ∈ wcel 2111 ∃!weu 2628 Vcvv 3441 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1797 ax-4 1811 ax-5 1911 ax-6 1970 ax-7 2015 ax-8 2113 ax-9 2121 ax-ext 2770 |
This theorem depends on definitions: df-bi 210 df-an 400 df-ex 1782 df-sb 2070 df-mo 2598 df-eu 2629 df-clab 2777 df-cleq 2791 df-clel 2870 df-v 3443 |
This theorem is referenced by: eueq2 3649 eueq3 3650 fsn 6874 bj-nuliota 34474 prprval 44031 |
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