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Mirrors > Home > MPE Home > Th. List > Mathboxes > bj-elissetALT | Structured version Visualization version GIF version |
Description: Alternate proof of elisset 2810. This is essentially the same proof as seen by inlining bj-denotes 36285 and bj-denoteslem 36284. Use elissetv 2809 instead when sufficient (in particular when 𝑉 is substituted for V). (Contributed by BJ, 29-Apr-2019.) (Proof modification is discouraged.) (New usage is discouraged.) |
Ref | Expression |
---|---|
bj-elissetALT | ⊢ (𝐴 ∈ 𝑉 → ∃𝑥 𝑥 = 𝐴) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | elissetv 2809 | . 2 ⊢ (𝐴 ∈ 𝑉 → ∃𝑦 𝑦 = 𝐴) | |
2 | bj-denotes 36285 | . 2 ⊢ (∃𝑦 𝑦 = 𝐴 ↔ ∃𝑥 𝑥 = 𝐴) | |
3 | 1, 2 | sylib 217 | 1 ⊢ (𝐴 ∈ 𝑉 → ∃𝑥 𝑥 = 𝐴) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 = wceq 1534 ∃wex 1774 ∈ wcel 2099 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1790 ax-4 1804 ax-5 1906 ax-6 1964 ax-7 2004 ax-8 2101 |
This theorem depends on definitions: df-bi 206 df-an 396 df-tru 1537 df-ex 1775 df-sb 2061 df-clab 2705 df-clel 2805 |
This theorem is referenced by: (None) |
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