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Mirrors > Home > MPE Home > Th. List > Mathboxes > bj-issetiv | Structured version Visualization version GIF version |
Description: Version of bj-isseti 36793 with a disjoint variable condition on 𝑥, 𝑉. The hypothesis uses 𝑉 instead of V for extra generality. This is indeed more general than isseti 3501 as long as elex 3504 is not available (and the non-dependence of bj-issetiv 36792 on special properties of the universal class V is obvious). Prefer its use over bj-isseti 36793 when sufficient (in particular when 𝑉 is substituted for V). (Contributed by BJ, 14-Sep-2019.) (Proof modification is discouraged.) |
Ref | Expression |
---|---|
bj-issetiv.1 | ⊢ 𝐴 ∈ 𝑉 |
Ref | Expression |
---|---|
bj-issetiv | ⊢ ∃𝑥 𝑥 = 𝐴 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | bj-issetiv.1 | . 2 ⊢ 𝐴 ∈ 𝑉 | |
2 | elissetv 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 1537 ∃wex 1777 ∈ wcel 2103 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1793 ax-4 1807 ax-5 1909 ax-6 1967 ax-7 2007 ax-8 2105 |
This theorem depends on definitions: df-bi 207 df-an 396 df-ex 1778 df-clel 2813 |
This theorem is referenced by: bj-rexcom4bv 36797 bj-vtoclf 36830 |
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