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Mirrors > Home > MPE Home > Th. List > Mathboxes > bj-isseti | Structured version Visualization version GIF version |
Description: Version of isseti 3460 with a class variable 𝑉 in the hypothesis instead of V for extra generality. This is indeed more general than isseti 3460 as long as elex 3463 is not available (and the non-dependence of bj-isseti 35345 on special properties of the universal class V is obvious). Use bj-issetiv 35344 instead when sufficient (in particular when 𝑉 is substituted for V). (Contributed by BJ, 13-Jun-2019.) (Proof modification is discouraged.) |
Ref | Expression |
---|---|
bj-isseti.1 | ⊢ 𝐴 ∈ 𝑉 |
Ref | Expression |
---|---|
bj-isseti | ⊢ ∃𝑥 𝑥 = 𝐴 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | bj-isseti.1 | . 2 ⊢ 𝐴 ∈ 𝑉 | |
2 | elisset 2819 | . 2 ⊢ (𝐴 ∈ 𝑉 → ∃𝑥 𝑥 = 𝐴) | |
3 | 1, 2 | ax-mp 5 | 1 ⊢ ∃𝑥 𝑥 = 𝐴 |
Colors of variables: wff setvar class |
Syntax hints: = wceq 1541 ∃wex 1781 ∈ wcel 2106 |
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 1913 ax-6 1971 ax-7 2011 ax-8 2108 |
This theorem depends on definitions: df-bi 206 df-an 397 df-tru 1544 df-ex 1782 df-sb 2068 df-clab 2714 df-clel 2814 |
This theorem is referenced by: bj-rexcom4b 35350 |
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