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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 2669. See euequ 2669 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 3602 | . 2 ⊢ (𝐴 ∈ V ↔ ∃!𝑥 𝑥 = 𝐴) | |
3 | 1, 2 | mpbi 222 | 1 ⊢ ∃!𝑥 𝑥 = 𝐴 |
Colors of variables: wff setvar class |
Syntax hints: = wceq 1656 ∈ wcel 2164 ∃!weu 2639 Vcvv 3414 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1894 ax-4 1908 ax-5 2009 ax-6 2075 ax-7 2112 ax-9 2173 ax-10 2192 ax-11 2207 ax-12 2220 ax-ext 2803 |
This theorem depends on definitions: df-bi 199 df-an 387 df-or 879 df-tru 1660 df-ex 1879 df-nf 1883 df-sb 2068 df-mo 2605 df-eu 2640 df-clab 2812 df-cleq 2818 df-clel 2821 df-v 3416 |
This theorem is referenced by: eueq2 3605 eueq3 3606 fsn 6657 bj-nuliota 33536 |
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